James L Farrell

A Look Back In Time 2023

Tue, 09 May 2023 19:59:46 GMT

This website has undergone an extensive overhaul in its mode of presentation. After years of being on the "back burner" the content will likewise receive modifications or deletions of outdated material, updates of existing material, plus additions absent until now because of other high-priority activities. Updating and addition has been a work in progress; this blog introduces some of the more important areas -- which I should have put somewhere on here earlier. Several external URLs (e.g., at zine sites that hosted columns I wrote) were subsequently changed, causing broken links, requiring correction. Admittedly the repairs haven’t been made often enough.

In regard to comments, trackbacks, link swap offers, etc. — I can’t keep up with deletions of all the extraneous ones. The only way to avoid being overrun is to disallow everything from outside from this point forward, with the contact page as the only exception. Spammers have “won” too many battles of this type, I realize, but administering penalties they deserve is a responsibility beyond my reach. The goal here, as always, is to provide useful info to those with an interest in areas where I’ve been privileged to work. An added observation: It may not be “SEO-friendly” to include, among blogs, tributes to individuals who have passed on. Nevertheless, I do that in special cases; giving credit where credit is due matters more.

A number of things I've advocated for decades are beginning to look possible. The main reasons for optimism include the following developments:

* Morton, J., Parkinson, B. W., Spilker, J. J., and van Diggelen, F. (Eds.), Gao, G. + Lo, S. (Assoc. Eds.), "Position Navigation & Timing technologies in the 21st Century", Wiley-IEEE 2020 was published near the end of 2020. After a quarter century the above second edition can replace the 1996 book -- also co-edited by father-of-GPS Brad Parkinson. Chapter 46 Part 2 contains my formulation + program + in-flight results for GPS/inertial integration.

* https://www.sae.org/publications/technical-papers/content/epr2020010/ and https://saemobilus.sae.org/content/EPR2020010/ are links for a 2020 report I put together with contributions from nine top experts. With the subject of unsettled topics in air traffic management it makes a compelling case for several fundamental changes, long overdue for Air Traffic Control. It addresses eight facets of ATM: Flight operations; Robustness/Resilience; Data validation; Data sharing (communications); Integration-vs-federation; Guidance strategies; Man/machine interface; Administration/coordination.

* At three National Advisory Board for satellite navigation meetings, in 2015 https://www.gps.gov/governance/advisory/meetings/2015-06/farrell.pdf , 2018 https://www.gps.gov/governance/advisory/meetings/2018-05/farrell.pdf , 2021 https://www.gps.gov/governance/advisory/meetings/2021-12/farrell.pdf , I discussed how those topics relate to safety.

* Safety takes center stage in my cover story for this year's first issue of InsideGNSS (January/February 2023). Among references cited therein are more detailed accounts of the relevant items and their history.

* After 40 years I received a written apology with a request (that I granted) to forgive a completely unjustified deception. Details will follow at a later time, but the issue was related to a video Antennas in Tracking Radar on this website (which cites another recent video, also directly relevant, on Air-to-Air Tracking).

* To that list I'll add breakthrough work on infrastructure early warning, based on evidence from gradual changes in shape that precede collapse. https://www.jameslfarrell.com/videos "Morphometrics for Early Warning" describes successful application of my 3D shape program to other operations (medical imaging and earthquake alert). Significant opportunity awaits.

2017-2019 IN REVIEW PRE-COVID

Sat, 11 Apr 2020 20:48:00 GMT

Apologies for little posting lately. Much activity included some with deadlines; this will focus primarily on the few years leading up to Covid.

For 2017 my involvement in the annual GNSS+ Conference again included teaching the two satnav/inertial integration tutorial courses with OhioU Prof. Frank vanGraas Also for the 2017 conference I wrote two manuscripts (with videos made to facilitate familiarization with the material), one for estimation and another providing opportunities for advanced warning .

2018 began with attendance at Cognizant Autonomous Systems for Safety Critical Applications (CASSCA). For that highlight I’ll note an insightful presentation by a speaker from Wright-Patterson Air Force Base (WPAFB): pilot override prevented F-16 crashes through automatic pullup; “artificial” intelligence (AI) isn’t completely artificial. For my own work, April meant presenting “New Interface Requirements: Implications for Future” at Integrated Communications Navigation and Surveillance (ICNS). Highlight of that conference was a rare acknowledgement, at high levels within Mitre and FAA, that past methods for collision avoidance are woefully inadequate for future air traffic (especially today with proliferation of pilotless vehicles). The two-part tutorial was again taught in Sept 2018.

The presentation just noted foreshadowed a sequel rendered again at the 2019 GNSS+ conference. Covid marked the end of that ten-year series. The interface topic, also reviewed in a May SAE International meeting, was presented during the same month to the National Space-based Advisory Board . For satnav/inertial integration, my GPS/inertial approach appears (plus sample results obtained with in-flight data) as Chapter 46 Part 2 , in a new satnav handbook edition again co-edited by father-of-GPS Brad Parkinson, first revised 25 years after its first appearance.

James L Farrell author of GNSS Aided Navigation and Tracking

Sat, 11 Apr 2020 20:34:00 GMT

GNSS Aided Navigation & Tracking

Dr. Farrell has many decades of experience in this subject area; in the words of one reviewer, the book is “teeming with insights that are hard to find or unavailable elsewhere.”

An engineer and former university instructor, Farrell has made a number of contributions to multiple facets of navigation. He is also the author of Integrated Aircraft Navigation (1976; five hard cover printings; now in paperback) plus over a hundred journal or conference manuscripts and various columns. Frequent aiding-source updates, in applications that require precise velocity rather than extreme precision in position, enables integration to be simplified. All aspects of integration are covered, all the way from raw measurement pre-processing to final 3-D position/velocity/attitude, with far more thorough backup and integrity provisions. Extensive experimental results illustrate the attainable accuracies (cm/s RMS velocities in three-dimensions) during flight under extreme vibration.

This book provides several flight-validated formulations and algorithms, in use but not yet widely because of their originality. Considerable opportunity is therefore offered in multiple areas including:

full use of highly intermittent ambiguous carrier phase
rigorous integrity for separate SVs
unprecedented robustness and situation awareness
high performance from low-cost IMUs
“cookbook” steps
new interoperability features
new insights for easier implementation.

It is our hope that you will find the new redesigned mobile website more informative and user friendly than our past one. Our intention is to offer visitors a fast loading, mobile ready, intuitive navigation and informative environment with not only factual and intense researched documents but video-driven information covering a broad spectrum of topics in specific areas including navigation, communication, data integrity, and tracking, applying modern estimation to data from various sources (COMM, gyros, accelerometers, GPS/GNSS, radar, optical, etc.). Another area, shape deformation analysis in 3-D, offers medical imaging advances plus early notification for earthquakes and infrastructure collapse as well.

For more information see the many blogs and videos on this website.

Activities over the past year

Thu, 30 Aug 2018 23:00:00 GMT

Apologies for little posting lately. Much activity included some with deadlines; this will be limited to the past twelve months. In 2017 my involvement in the annual GNSS+ Conference again included teaching the satnav/inertial integration tutorial sessions with OhioU Prof. Frank vanGraas. Part I and Part II were likewise offered for Sept 2018. Also for the 2017 September conference I wrote two manuscripts (with videos made to facilitate familiarization with the material), one for estimation and another providing opportunities for advanced warning .

For 2018 this will allow space for just one or two items from each event mentioned. The year began with attendance at Cognizant Autonomous Systems for Safety Critical Applications (CASSCA). For that highlight I’ll note an insightful presentation by a speaker from Wright-Patterson Air Force Base (WPAFB): pilot override prevented F-16 crashes through automatic pullup; “artificial” intelligence (AI) isn’t completely artificial. For my own work, April meant presenting “New Interface Requirements: Implications for Future” at Integrated Communications Navigation and Surveillance (ICNS). Highlight of that conference was a rare acknowledgement, at high levels within Mitre and FAA, that past methods are woefully inadequate for future air traffic needs.

The presentation just noted foreshadowed a sequel scheduled for a subsequent conference . The interface topic, also reviewed in a May SAE International meeting, was presented during that same month to the National Space-based Advisory Board . For the satnav/inertial integration topic, I recently completed my Chapter 46 Part 2 that appears in a new edition of the satnav handbook co-edited by father-of-GPS Brad Parkinson; revised 25 years after its 1996 original version.

Inst. of Navigation GNSS Tutorials

Thu, 28 Jun 2018 18:20:00 GMT

For the decade ending with Covid (2019) I was privileged to work with Ohio University Prof. Frank vanGraas, in presenting tutorial sessions at Institute of Navigation’s annual GNSS conference. Two sessions covered integrated navigation with Kalman filtering.

By way of background : The first session was introductory, with each attendee being given a book with a development aimed at those learning inertial navigation and/or Kalman filtering for the first time . Prior to the course, my free-to-ION-members online tutorial was recommended. Also my three-part matrix tutorial video was made freely available to attendees.

Prof. vanGraas sponsored, and provided the flight data that enabled, the successful validation of 1-cm/sec RMS velocity vector accuracy obtained from 1-second sequential changes in carrier phase . Those results for almost an hour in air are provided, with the algorithms used to obtain them, in a more recent book that was given to those attending the second session. Importance of this material has increased further with ongoing Standards Development described in my recent presentation to the National Advisory Board for satnav.

TWO PILLARS OF OUR INDUSTRY’S EXPERTISE

Mon, 30 Apr 2018 20:31:00 GMT

TWO PILLARS OF OUR INDUSTRY'S EXPERTISE
The Institute of Navigation's GNSS+ 2018 Conference provided me the privilege of collaborating with two of the industry's pillars of expertise. Professor Frank van Graas from Ohio University and I taught integration of inertial and satellite navigation via modern estimation. Then on the last day of the conference I'm coauthored with William Woodward, Chairman of SAE International Aerospace Avionics Sys Div and hardware lead for next generation Resilient EGI (abstract at https://www.ion.org/publications/search.cfm?publication=GNSS&year
=2018&title=&author=woodward&searchText=&searchIn=abstract ). The paper, our strong response to obstacles confronting position, navigation and timing (PNT) from a large and growing array of challenges, describes
* a frank assessment of our industry's glacial response to those challenges
* a fundamental step in the direction toward mitigating those obstacles
* how that step will enable several innovations discussed on this website.

Opening of Doors Previously Riveted Shut

Tue, 24 Apr 2018 01:59:00 GMT

A new SAE standard for GPS receivers is a natural complement to a newly receptive posture toward innovation unmistakably expressed at high levels in FAA and Mitre (ICNS 2018). Techniques introduced over decades by this author (many on this site) can eventually become operational.

1980s euphoria over GPS success was understandable but decision-makers, lulled into complacency, defined requirements in adherence to antiquated concepts. Familiar examples (full-fix-every-time, with emphasis on position irrespective of dynamics) only begin a broad range revealing opportunities long deferred. “Keep it simple” produced decades of over simplification, strangling efforts to overcome adversity. “Integration” became a misnomer, inappropriately bestowed as “legacy systems” slavishly followed paths precluding resilience.

Not all of the issues presented to the National Advisory Board for Satellite Navigation in 2015) are obvious, even to experienced designers. A crucial point is insight (the video under that title provides an illustration outside the realm of navigation) , without which even a mathematically flawless formulation and program can fail operationally; real-world examples illustrating that point are included in coursework described below.

As widely accepted procedures are finally considered open to revision, courses taught by this author offer capabilities needed over a wide range (inertial, magnetometer, radar, optical, GPS pseudorange, carrier phase, … ).

Comments by former Inst-of-Navigation presidents ( no stone unturned ; teeming with insights that are hard to find or unavailable elsewhere … ) are likewise true of the course material which, in common with the book (provided as part of the advanced course registration), has a major focus on robustness so urgently needed in coming developments for navigation plus myriad modes of tracking as well).

SAE Standard for GPS Receivers

Thu, 22 Mar 2018 22:56:00 GMT

At the April 2018 ICNS meeting (Integrated Communications Navigation and Surveillance) as coauthor with Bill Woodward (Chairman, SAE International Aerospace Avionics Systems Division), I presented " NEW INTERFACE REQUIREMENTS: IMPLICATIONS for FUTURE " . By " future " we indicate the initiation of a task to conclude with a SAE standard that will necessitate appearance of separate satellite measurements to be included among GPS receiver outputs. Content of the presentation includes flight-validated dramatic improvements in multiple facets applicable to air traffic control (e.g., reduction in area of uncertainty at closest approach, by factors on the order of a million ; major enhancement of achievable integrity, availability, etc.) — accessible from public domain with no requirements for scientific breakthroughs or new inventions. All benefits are derived from exploiting capabilities that have been available for decades, by discarding outdated practices devised largely to accommodate limitations in yesteryear’s provisions.

Although my writings for years expressed advocacy for these dormant advantages, concrete action was limited to embedded (often proprietary, inflexible) systems plus a modest number of scattered ventures, rather than widespread acceptance offering high accuracy at low cost. Dominance of simplified methods with huge performance penalty continues to this day, despite urgent need to cope with challenges to satellite navigation. For release from this “grip-of-inertia” a standard will mandate presence of individual satellite measurements at receiver output interfaces. The most obvious effect, ability to make use ( finally ! ) of partial data, is only the beginning of a benefit list; advances in main pillars of performance criteria (accuracy, availability, integrity, and continuity) can be intense enough to reconsider some definitions.

Enhancements will materialize not only in aircraft — in air or on ground — but in maritime operation and land vehicles as well, whether manned or unmanned. Future extensions could involve other sensors. The purpose is empowerment of users through removal of constraints currently inhibiting robustness/resilience. Immediately it is acknowledged — none of this will matter without victory in another area: security. The battle of the spectrum and subsequent authentication must be won first. As I noted in an earlier forum , everything I’ve advocated all this time is not a replacement for but a recommended addition to that important work. As satnav cannot exist without authentic data, it cannot be resilient without raw data.

1-page summary

Measurements from GPS and GNSS

Sat, 16 Jul 2016 21:58:00 GMT

A recent video describes a pair of long-awaited developments that promise dramatic benefits in achievable navigation and tracking performance. Marked improvements will occur, not only in accuracy and availability; over four decades this topic has arisen in connection with myriad operations, many documented in material cited from other blogs here.

REASONS for INACTION — and CONSEQUENCES

Fri, 12 Feb 2016 22:40:00 GMT

For reasons, consider a line from a song in Gilbert-&-Sullivan’s Gondoliers :
“ When everybody is somebody, then nobody is anybody ” — (too many cooks)

For consequences, consider this question:
Should an intolerable reality remain indefinitely intolerable ?

While much of the advocacy expressed in my publications and website have focused on tracking and navigation, this tract concentrates instead on two major opportunities to apply a breakthrough solution that is virtually unknown.

60 Minutes alerted the public to an intolerable reality. Rather than repeating description of that problem I’ll jump immediately to the basis for my recommendation:
* Structures change shape before they fail.
* Changes in shape offer advanced warning.
* Reinforcement can be prescribed only for those exhibiting the warnings.
* Shape can be deduced from sets of measurements that are already in place.
* Those results can be acquired from computers processing all day every day.
* Neither computation nor data transmission to a central hub would be costly.
* Classical shape state analysis, limited to 2-D, has been extended to 3-D.
* That 3-D extension has already been validated by using GPS measurements.
* Hardly anyone knows that the 3-D extension happened.
* In fact, most techies are unfamiliar with shape states, even in 2-D.

Only the 7th and 8th items need any elaboration. The latter can be verified, in varying degrees of detail, through sources cited now. First, Figure 2 of a 3-page summary provides a quick glance. Those wanting more in-depth description can access a full manuscript with real data for verification . There’s also a blog concentrated on application to earthquakes.

The remaining item needing explanation is covered here in terms of a video describing 3D Deformation Extraction for Morphometrics . Those who follow it will see that the most widely known authoritative source is limited to two dimensions. Obviously the 3-D extension is essential for applications being described here (and in fact, even for accurate imaging — genesis from that field is incidental; subordinate to the present purpose). Further discussion of promise for anticipating structural failure appears in another blog .

Support for this work has been limited to (a)medical imaging verification and (b)a trip to present the quake data results. My voice can be heard in forums on navigation and tracking but, evidently, not by those responsible for safety in presence of structural dangers. I’m not claiming completion of everything required for operational readiness but, with no action at all, an intolerable reality will remain indefinitely intolerable. Seventy thousand bridges won’t be repaired any time soon but, with advanced knowledge where needed, the cost of essential action can be minimized. Continuous shape state computations fed by already in-place monitoring data could likewise give life-saving warnings.

Commercial value of this capability could be enormous, but a far better plan would be a low-cost pilot program with a lion’s share of eventual gain steered directly toward a worthy charity (one with a favorable rating from CharityWatch ). I have no idea how to make that happen. Someone in a position of authority, with no ambition to become the next billionaire, could conceivably define a workable strategy.

COLLISION AVOIDANCE: HELP URGENTLY NEEDED

Tue, 08 Dec 2015 16:23:00 GMT

Let me begin with a quote worth repeating — “Do we really need to wait for a catastrophe before taking action against GNSS vulnerabilities ?” — and follow with an extension of scope beyond.

It’s encouraging to see LinkedIn discussions recognizing ADSB limitations that preclude dependable collision avoidance capability – but that recognition needs to be far more widespread. The limitations are both severe and multifaceted including, in addition to vulnerability from inadequate security,

* accuracy goals based on present position instead of the monumentally more important relative velocity — ADSB allows 10 meter/sec velocity error (!), without characterization as vectorial or relative or probabilistic.

* the glaring but near-universal flaw of sharing coordinates, thereby failing to exploit what made differential operation spectacularly successful: work with individual measurements separately.

Note that these deficiencies existed long before the emergence of unmanned vehicles. The need to correct them is as fundamental as it is urgent. I’ve communicated these concerns over and over, most recently receiving a gratifying response from my June 11 presentation to the satnav National Advisory Board , with details available from URLs at the end.

In that presentation I cited a successful flight validation achieving accuracy on the order of cm/sec, for the crucially important relative velocity between vehicles that can be on or near a collision course. That is a thousand times less error than the 10 meter/sec allowed by ADSB. Furthermore, reduction by a thousand in each of two directions translates into a million times less area of uncertainty. To realize this crucial safety improvement no new discoveries are needed and no new equipment needs to be invented; only the content of transmitted data needs to change: measurements rather than coordinates. Yet usage of the method is not being planned. After initially proposed before 2000, a limited support program started circa 2010 is the only step taken toward this direction.

No claim is made that the last word has been spoken or that introduction of the needed modifications — nor accompanying regulation — would be trivial. The intent here is not criticism and complaints for the sake of criticism and complaints. Emphasizing unwelcome reality always caries risk of drawing wrath. Nevertheless, especially now with growing usage of unmanned vehicles, sounding an alarm is better than passively waiting for a calamity. So here’s an alarm: Inadequate preparation for collision avoidance is a microcosm of a much wider overall flaw in today’s decision-making process. For years substantial numbers of qualified people have spent extensive effort trying to prevent cataclysmic failures in one area or another involving PNT (position/navigation/timing). They definitely deserve attention and action.

Anything approaching a thorough compilation of worthy advocacy would require considerable length; just a few recent examples are cited here. Explanations tracing inaction to current shortcomings can logically include a diagnosis of dissatisfaction expressed at a pinnacle of authority within DoD . An even more current offering is only the latest expression of regret over insufficient support for satnav, describing a highly relevant chain of inaction over a multiyear period. Near the beginning of that period, a cover story for Coordinates magazine repeated a quote from the previous month’s cover story The quote worth repeating, cited at the start of this, is a perfect expression of the frustration prevalent over a decade following the universally acclaimed 2001 Volpe report. Now, almost a decade-and-a-half after that report, partial progress toward a solution coexists with minimal progress toward collision avoidance — while unmanned vehicles are already threatening passenger flight safety. Now to extend the quote: “Do we really need to wait for a catastrophe before making better use of measurements — GNSS or otherwise — to prevent collisions in the presence of increased manned and unmanned traffic?”

Earth Rotation Adjustment for GPS/GNSS

Sat, 07 Nov 2015 16:22:00 GMT

A cursory glance at the GPS/GNSS adjustment for Earth rotation has placed a question in the minds of some analysts, wondering how that squares with Einstein. Speed of light invariance means that motion of the earth during
transit cannot affect a signal’s time of arrival. By making the adjustment implicit rather than explicit in the pseudorange expression, and enforcing coordinate frame consistency for vector subtraction, the paradox is resolved. The reasoning used here applies to satellite motion as well, but the point being made can be illustrated by focusing on Earth rotation only.
The compact form in
* Eq. (2.58) of GNSS Aided Navigation & Tracking and in
* the explanation of double differences on this site uses that concept, plus a common practice of including the full relativistic adjustment in the satellite clock correction.

A recent video discusses these issues while also explaining reliance of the book just cited on earlier references. The advantage of that reliance is brevity plus minimum distraction for readers already familiar. Inevitably there is an accompanying disadvantage; those lacking familiarity will have a perception of incompleteness. To close the gap, the first chapter cites

* three widely acclaimed references for satellite navigation, far more thorough than paraphrasing could have provided

* a pre-GPS book Integrated Aircraft Navigation covering fundamentals of Kalman filtering and inertial navigation.

GRATIFYING RESPONSES

Wed, 26 Aug 2015 02:46:00 GMT

After wide distribution of my recent Inside GNSS letter I’ve received very encouraging responses from a number of heavy hitters. There have always been knowledgeable individuals agreeing with the points raised therein, but current conditions offer an increased sense of urgency. With uncertainty of support for vital resources, a real-world precedent (five years without LORAN), and a Defense Secretary who hates GPS , my impulse toward advocacy has grown more determined; in fact, crystallized. Not everyone will welcome this, but it w ill go down much easier if viewed as a vital opportunity, Here goes.

Among the methods awaiting basic modification for navigation and tracking, one is especially glaring: the ubiquitous practice of sharing coordinates. Those familiar with my work know me as a relentless advocate (in print, since 1977) of sharing raw measurements instead of coordinates. The seemingly unremarkable character of that step is deceptive; despite its operational simplicity, the resulting improvements would be profound. For quick verification of that claim recall how major errors cancel (from each satellite separately of course) in differential GPS — and that’s only the beginning.

As important as accuracy is, additional performance traits of equal importance are also dramatically affected. Without separate measurements, integrity testing can’t be done. Furthermore, with partial data usage, two more main performance criteria (availability & continuity) would be vastly improved — in fact, calling for their redefinition to account for the immense benefit.

The list of reasons (rigorous accounting for correlations as well as different statistics of errors in different directions, at different times, from sensors with different tolerances; immunity of scalar measurements to an occasionally misconstrued reference datum etc.) continues on and on. Among those not yet mentioned here, I now choose an especially important feature for illustration: ability to achieve precise dynamics. Flight tests by Ohio University produced cm/sec velocity residuals for navigation ( GNSS Aided Navigation & Tracking , with results in Chapter 8 and public domain algorithms in earlier chapters), then later for tracking — a THOUSAND times better than ADSB’s 10 meter/sec. It’s not as if we didn’t know how to accomplish these objectives. We’ve known how to combine myriad data sources, sequentially and optimally, for well over a half-century. Yet even now, given information from two different subsystems (e.g., GNSS and DME), how are they processed now? Either internally (and invisibly in costly inflexible embedded systems) or externally by averagin g
coordinates. A most elementary example highlights futility of the latter: imagine data from one sensor offering precise latitude and extremely degraded longitude — mixed with another offering the opposite.

The fundamental nature of these reasons is matched by an equally fundamental course of action needed to achieve the requisite goals: simply replace data bits in standard messages. No scientific breakthroughs nor hardware redesigns — just change what’s transmitted by UAT or Mode-S extended squitter messages. Most of the content (preamble, error correction, etc.) can remain unchanged; just replace information bits (latitude, longitude, etc.) by measurements.

The case is quite compelling for application of known methods, to not only satnav but all sources of data to be used in navigation and tracking. All benefits will become reality if we adopt, VERY belatedly, the basic step recommended in the title of a 1999 publication

Defense Secretary “hates GPS”

Sat, 08 Aug 2015 20:57:00 GMT

Secretary of Defense Ashton Carter’s recent statement “I hate GPS” naturally creates much concern within the navigation community. The July-August issue of Inside GNSS contains his presentation with the reaction from editor Glen Gibbons, plus my own response which delineates
* where the Secretary is badly mistaken, and
* where his concerns are legitimate.
There is a connection between the latter and our industry’s decades-long determined resistance to common-sense improvements in both performance and economy. Steps offering dramatic benefits are further described in material long available from this site. Rather than repeat those descriptions here, I now focus instead on another kind of avoidance: an urgent need to swerve away from another administrative blunder .

Recent history illustrates how the preceding expression is no exaggeration. Loss of LORAN wasn’t permanent, for reasons that were primarily capricious. Planned destruction of vital backup to a vulnerable pillar for communication and navigation wasn’t completed because the government never got around to finishing it. Hundreds of experienced professionals offered testimony in 2009 (including my “two cents’ worth” revisited ) — which failed at the time. Administrative action shut down LORAN for years, with intent to destroy it.

Poor judgment, however, is not the sole cause of unwise administrative action. Often it is prompted by poor performance; the GAO-08-467SP report provides a perfect explanation of that. Dismal as it is, it must be believed that even gross departures from responsible stewardship can be corrected. Destroying a critical resource is obviously not the answer.

MONUMENTAL IMPROVEMENTS for GNSS

Sat, 13 Jun 2015 20:43:00 GMT

A long list of steps furthering satellite navigation progress can be envisioned from the agenda covering eight hours in 2015's

June 11 gathering of the National Space-Based Positioning, Navigation, and Timing Advisory Board . Toward the end of the

day I was privileged to present my recommendations toward those objectives.

HOW NOT TO DO LOOSE GNSS/IMU COUPLING

Thu, 29 Jan 2015 19:56:00 GMT

An article I wrote offers a critique explaining why a common method used for satnav/inertial coupling can defeat the purpose of using inertial data at a ll.

What’s New? — A pledge fulfilled

Wed, 21 Jan 2015 03:14:00 GMT

A review described my 2007 book as “teeming with insights that are hard to find or unavailable elsewhere” — I hasten to explain that the purpose wasn’t to be different for the sake of being different. With today’s large and growing obstacles placed in the way of satellite navigation, unusual features of my approach were motivated primarily by one paramount objective: robustness. Topics now to be addressed are prompted largely by a number of LinkedIn discussions. In one of them I pledged that my unusual-&-unfamiliar methods, adding up to a list of appreciable length, would soon be made available to all. This blog satisfies that promise, in a way that is more thorough than listings offered previously. I’ll begin with innovations made in my earlier (pre-GPS) book Integrated Aircraft Navigation . That book’s purpose was primarily educational; learning either inertial navigation or Kalman filtering from any/all literature existing in the mid-1970s was quite challenging (try it if you’re skeptical). Still it offered some features originating with me. Chief among those were

* extension of previously known precession analysis, following through to provide a full closed form solution for the attitude matrix vs time (Appendix 2.A.2)
* extension of the previously known Schuler phenomenon, following through to provide a full closed form solution for tilt and horizontal velocity errors throughout a Schuler period (Section 3.4.2), and reduction to intuitive results for durations substantially shorter
* an exact difference in radii, facilitating wander azimuth development that offers immunity to numerical degradation even as the polar singularity is reached and crossed (Section 3.6)
* analytical characterization for average rate of drift from pseudoconing (Section 4.3.4), plus connection between that and the gyrodynamics analysis preceding it with the classical (Goodman/Robinson) coning explanation
* expansion of the item just listed to an extensive array of motion-sensitive errors for gyros and accelerometers, including rectification effects (some previously unrecognized) in Chapter 4
* Eq. (5-57) with powerful ramifications for the level of process noise spectral density (which, without a guide, can otherwise be the hardest part of Kalman filter design) .

The list now continues, with innovations appearing in the 2007 book —
* Eq. (2.65), in correspondence to the last item just identified — with follow-through in Section 4.5 (and also with history of successful usage in tracking operations)
* Section 2.6, laying a foundation for much material following it
* Eqs. (3.10-3.12), again showing wander azimuth immune to numerical degradation
* Section 3.4.1 for easier-than-usual yet highly accurate position (cm per km) incrementing in wander azimuth systems
* first bulleted item on the lower half of p.46, which foreshadows major simplifications in Kalman filter models that follow it
* Table 4.2, which the industry continues to ignore — at its peril when trying to enable free-inertial coast over extended durations
* sequential changes in carrier phase (Section 5.6, validated in Table 5.3) — and how it relieves otherwise serious interoperability problems (Section 7.2.3), especially if used with FFT-based processing (Section 7.3)
* single-measurement RAIM, Section 6.3
* computational sync, Section 7.1.2
* tracking applications (Chapter 9, also validated in operation) with emphasis on identifying what’s common — and what isn’t — among different operations
* realistic free-inertial coast characterization and capabilities, Appendix II
* practical realities, Appendix III
* my separaton of position from dynamics + MANY ramifications
* commonality of track with short-term INS error propagation (Section 5.6.1)

There are more items, e.g., various blogs from this website, which can be helpful also in pointing out other descriptions e.g., 1-sec carrier phase usage

CRUMBLING INFRASTRUCTURE: A SOLUTION?

Tue, 25 Nov 2014 22:32:00 GMT

On 11/23/14, 60 Minutes drew wide attention to neglect of U.S. infrastructure, correctly attributing this impending crisis to inexcusable dereliction of duty. I won’t claim authority to straighten out our politicians but I can offer a way to light a fire under them: suppose they were given evidence, known also to the public, about how a collapse often happens slowly enough to allow advanced warning. A method already successful in two different applications could be applied for infrastructure as well. Now s e e the title " ShapeVid" among the videos on this website.

Earthquake Analysis by 3-D Affine Deformations

Sat, 06 Sep 2014 15:30:00 GMT

Changes in coordinates at stations affected by earthquakes have been monitored successfully, for years, with precision using satellite navigation. Results of interest have then been produced in the past by processing the outcome, e.g., investigating the history of triangles formed thereby. The first application to earthquakes of entirely different criteria (affine deformation states) has produced results with encouraging prospects for prediction, both in time (more than two weeks prior to the 2011 Tohoku quake) and spatially (departures from the affine model at the station nearest epicenter).

The fifteen independent states of a standard 3-D 4×4 affine transformation can be categorized in five sets of three, each set having x-, y-, and z-components for translation, rotation, perspective, scaling, and shear. Immediately the three degrees-of-freedom associated with perspective are irrelevant for purposes here. In addition both translation and rotation, clearly having no effect on shape, can be analyzed separately — and the same is likewise true of uniform scaling. It is thus widely known that there are five “shape states” involved in 3-D affine deformation, three for shear and two for nonuniform scaling. One way to describe shape states is to note their effects in 2-D, where there is only one for nonuniform scaling (which deforms a square into a rectangle) and one for shear (which deforms a rectangle into a parallelogram). Therefore it is noted here that added insight into earthquake investigation can be obtained by analyzing affine features – with specific attention given to their individual traits (degrees-of-freedom).

For investigating earthquakes from affine degrees-of-freedom, methodology of another very different field — anatomy — is highly relevant but ironically lacking a crucial feature. As currently practiced, physiological studies of affine deformations concentrate heavily on two-dimensional representations. While full affine representation is very old, its inversion — i.e., optimal estimation of shape states from a given overdetermined coordinate set — has previously been limited to 2-D.

Immediately then, extension was required for adaptation. The fundamentals, however, still remain applicable. Instead of designated landmark sets coming from a group of patients, here they are associated with a series of days (e.g., from several days before to some days after a quake). Each landmark set is then subjected to a series of procedures (centroiding, normalization, rotation) for fitting landmark sets from one day to another.

The Procrustes representation from procedural steps just described provides sequences of centroid shifts in each direction, rotations about each axis, and amounts of uniform scaling needed for each separate day. In addition to those seven time histories, there are five more that offer potential for greater insight (again, shape states — three shear and two nonuniform scaling). All were obtained for landmark coordinate sets reported before and after the 2011 Tohoku quake. From sample recorded coordinates provided along with shape state values, readers of the manuscript are enabled to verify results.

Matrix Theory for Modern Estimation

Sun, 08 Jun 2014 17:49:00 GMT

Recent videos providing just enough matrix theory needed for Kalman filtering are available for those attending courses I teach (to allow review of limited time covering it in class). The one-hour presentation is divided into three sections, each with a preview.

The first section, with very little math, begins by explaining why matrices are needed — and then immediately emphasizes that MATH ALONE IS NOT ENOUGH. To drive home that point, a dramatic illustration was chosen. Complex motions of a satellite, though represented in a MATHEMATICALLY correct way, were not fully understood by its designers nor by the first team of analysts contracted to characterize it. From those motions, shown with amplitudes enlarged for easy visualization, it becomes clear why insight is every bit as important as the math. That one word insight -- the title of a video on this website -- justifies all efforts to master this material.

The matrix presentation supplies theoretical prerequisites that will assist aspiring designers in formulating linear(ized) estimation algorithms in block (weighted least squares) or sequential (recursive Kalman/EKF) form. Familiar matrix types (e.g., orthogonal, symmetric), their properties, how they are used — and why they are useful — with interpretation of physical examples, enable important operations both powerful and versatile. An enormous variety of applications involving systems of any order can be solved in terms of familiar expressions we learned as teenagers in college.

Surveillance with GPS/GNSS

Wed, 12 Mar 2014 04:22:00 GMT

The ago-old Interrogation/Response method for air surveillance was aptly summarized in an important 1996 GPSWorld article by Garth van Sickle: Response from an unidentified IFF transponder is useful only to the interrogator that triggered it. That author, who served as Arabian Gulf Battle Force operations officer during Desert Storm, described transponders flooding the air with signals. Hundreds of interrogations per minute in that crowded environment produced a glut of r-f energy – but still no adequate friendly air assessment.

The first step toward solving that problem is a no-brainer: Allocate a brief transmit duration to every participant, each separate from all others. Replace the Interrogation/Response approach with spontaneous transmissions. Immediately, then, one user’s information is no longer everyone else’s interference; quite the opposite: each participant can receive every other participant’s transmissions. In the limit (with no interrogations at all), literally hundreds of participants could be accommodated. Garble nonexistent. Bingo.

Sometimes there a catch to an improvement that dramatic. Fortunately that isn’t true of this one. A successful demo was performed at Logan Airport – using existing transponders with accepted data formatting (extended squitter), in the early 1990s, by Lincoln Labs. I then (first in January 1998) made two presentations, one for military operation (publication #60- click here ) and another one for commercial aviation (publication #61-click here ), advocating adoption of that method with one important change. Transmitting GPS pseudoranges rather than coordinates would enable an enormous increase in performance. Reasons include cancellation of major errors – which happens when two users subtract scalar measurements from the same satellite, but not coordinates formed from different sets of satellites. That, however, only begins to describe the benefit of using measurements ( publication #66 ); continue below:

With each participant receiving every other participant’s transmissions, each has the ability to track all others. That is easily done because (1) every extended squitter message includes unique source identification, and (2) multiple trackers maintained in tandem have been feasible for years; hundreds of tracks would not tax today’s computing capability at all. Tracks can be formed by ad hoc stitching together coordinate differences, but accuracy will not be impressive . A Kalman tracker fed by those coordinate differences would not only contain the uncancelled errors just noted, but nonuniform sensitivities, unequal accuracies, and cross-axis correlations among the coordinate pseudo measurement errors would not be taken into account. Furthermore, the dynamics (velocity and acceleration) – as derivatives – would degrade even more – and dynamic accuracy is absolutely crucial for ability to anticipate near-future position (e.g., for collision avoidance).

The sheer weight of all the considerations just noted should be more than enough to motivate the industry towards preparing to exploit this capability. But, wait – there’s more. Much more, in fact. For how many years have we been talking about consolidating various systems, so that we wouldn’t need so many different ones? Well, here’s a chance to provide both 2-dimensional (runway incursion) and 3-dimensional (in-air) collision avoidance with the same system. The performance benefits alone are substantial but that plan would also overcome a fundamental limitation for each –
* Ground: ASDE won’t be available at smaller airports
* In-air: TCAS doesn’t provide adequate bearing information; conflict resolution is performed with climb/dive.
The latter item doesn’t make passengers happy, especially since that absence of timely and accurate azimuth information prompts some unnecessary “just-in-case” maneuvers.

No criticism is aimed here toward the designers of TCAS; they made use of what was available to them, pre-GPS. Today we have not just GPS but differential GPS. Double differencing , which revolutionized surveying two decades ago, could do the same for this 2-D and 3-D tracking. The only difference would be absence of any requirement for a stationary reference. All positions and velocities are relative – exactly what the doctor ordered for this application.

OK, I promised – not just more but MUCH more. Now consider what happens when there aren’t enough satellites instantaneously available to provide a full position fix meeting all demands (geometry, integrity validation): Partial data that cannot provide instantaneous position to be transmitted is wasted (no place to go). But ancient mariners used partial information centuries ago. If we’re willing to do that ourselves, I’ve shown a rigorously derived but easily used means to validate each separate measurement according to individual circumstances. A specific satellite might give an acceptable measurement to one user but a multipath-degraded measurement to another. At each instant of time, any user could choose to reject some data without being forced to reject it all. My methods are applicable for any frequency from any constellation (GPS, GLONASS, GALILEO, COMPASS, QZSS, … ).

While we’re at it, once we open our minds to sharing and comparing scalar observations, we can go beyond satellite data and include whatever our sensors provide. Since for a half-century we’ve known how to account for all the nonuniform sensitivities, unequal accuracies, and cross-axis correlations previously mentioned, all incoming data common to multiple participants (TOA, DME, etc.) would be welcome.

So we can derive accurate cross-range as well as along-range relative dynamics as well as position, with altitude significantly improved to boot. Many scenarios (those with appreciable crossing geometry) will allow conflict resolution in a horizontal plane via deceleration – well ahead of time rather than requiring a sudden maneuver. GPS and Mode-S require no breakthrough in inventions, and track algorithms already in public domain carry no proprietary claims. Obviously, all this aircraft-to-aircraft tracking (with participants in air or on the ground) can be accomplished without data transmitted from any ground station . All these benefits can be had just by using Mode-S squitter messages with the right content .

There’s still more. Suppose one participant uses a different datum than the others. Admittedly that’s unlikely but, for prevention of a calamity, we need to err on the side of caution; “unlikely” isn’t good enough. With each participant operating in his own world-view, comparing scalar measurements would be safe in any coordinate reference. Comparing vectors with an unknown mismatch in the reference frame, though, would be a prescription for disaster. Finally, in Chapter 9 of GNSS Aided Navigation & Tracking I extend the approach to enable sharing observations of nonparticipants.

In the About panel of this site I pledged to substantiate a claim of dramatic improvements afforded by methods to be presented. This operation is submitted as one example satisfying that claim. Many would agree (and many have agreed) that the combined reasons given for the above plan is compelling. Despite that, there is no commitment by the industry to pursue it. ADSB is moving inexorably in a direction that was set years ago. That’s a reality – but it isn’t the only reality. The world has its own model; it doesn’t depend on how we characterize it. It’s up to us to pattern our plans in conformance to the real world, not the other way around. Given the stakes I feel compelled to advocate moving forward with a pilot program of modest size – call it “Post-Nextgen” – having the robustness to recover from severe adversity. Let’s get prepared.

WANTED: PRECISE VELOCITY — UNMANNED or NOT

Fri, 17 Jan 2014 18:58:00 GMT

Recent and current posts have expressed concern, serious to anyone who envisions future air traffic prospects. Those concerns stemmed from events preceding further developments adding more disquiet. Consider this “triple-whammy:

* prospect for tripling of air traffic
* addition of UAVs into NAS
* ADSB methodology plans

Now add all implications of a headline from 2013: GAO Faults DHS, DoT for GPS Interference/Backup Effort in that year-end description a friend of mine (Terry McGurn) is quoted, saying “I don’t know who’s in charge.” That thoroughly credible diagnosis, combined with subsequent observations by father-of-GPS Brad Parkinson, crystallizes in many minds an all-too-familiar scenario with a familiar prospective outcome: The steps they’ve correctly prescribed “can’t” be implemented now. It’s “too late” to change the plan — until “too late” acquires a new meaning (i.e., too-late-to-undo-major-damage).

Historically this writer has exerted considerable effort to avoid dramatizing implications of the status quo. While straining to continue that effort, I feel compelled to highlight those implications related to air safety.

OK there will be no naming names here, but many with influence and authority do “not believe that the minimum performance required by the ADS-B rule presents a significant risk to the operation of the National Airspace.” Here’s my worry:
* That minimum required performance allows ten meters/second velocity error
* Efforts to provide precise position therefore become ineffective within an extremely short time

* What translates into collision avoidance isn’t present Lat/Lon but future relative position accuracy
* Consequently the accuracy that matters isn’t in position but in velocity relative to every potentially conflicting object

* Each of those relative velocities can be in error by 10 m/sec or more in more than one direction

* Guidance decisions made for collision avoidance must be prepared in advance
* TCAS sudden climb/dives (which produced a news story about screaming passengers), plans a minute and a half ahead
* With 10 m/sec velocity error that gives 900 meters uncertainty in projected miss distance — just simple arithmetic
* That simple calculation is very far from being a containment limit
* Only containment limits based on conservative or realistic statistics can provide confidence for safety

* 3 sigma (even 10 sigma) containment limits don't give low enough collision probability with non-gaussian distributions

Combined weight of these factors calls for assessment of prospects with future (tripled) air traffic plus UAVs. It has been asserted that, rather than ten m/sec, one m/sec is much more likely. As noted earlier, “much more likely” is far from sufficient reassurance. Furthermore, multiplying time-to-closest-approach by 1 m/sec, and amplifying that result by enough to produce a credible containment limit, still produces unacceptably large uncertainty in projected miss distance. So: expect (1) either frequent TCAS climb/dives or (2) guidance commands generated for safe separation resulting in enormous deviations from what’s really needed. Forget closer spacing.

Add to that runway incursions, well over a thousand per year and increasing — also with everything said about needs for avoiding other objects applicable to maritime (shoals) as well as airborne conflicts; Amoco-Cadiz, Exxon-Valdez, … .

These points are covered by presentations and documentation from decades back. The best possible sense-&-avoid strategy is incomplete without precise relative ( not absolute ) future (i.e., at closest approach, not current ) position — which translates into velocity accuracies expressed in cm/sec ( not meters/sec ). The industry has much to do before that becomes familiar — let along the norm that containment requires. A step in this direction is offered by in-flight result s validating the accuracy traits just described.

How reliable is reliable enough?

Sat, 14 Dec 2013 01:14:00 GMT

GPS is by far the best-ever system for both navigation and timing. Recognition of that is essentially universal. Less widely recognized are the ramifications of growing dependence on GPS, in both communications and navigation. This discussion will concentrate on the latter, highlighting attendant risk in flight. Although extensive deliberation already exists, I’ll presume to offer my experience. Immediately it is acknowledged that the risk is low; but now let’s ask what is low enough. While every effort is made here to avoid an alarmist tone, answering that question calls for an unflinching look at potential consequences if the gamble ever failed.

The above paragraph opens a broader (two-page) discussion on this same site . That expanded discussion addresses several familiar topics; GPS, for example, lives up to expectations, brilliantly performing as advertised. Since no system can be perfect, the industry uses firmly established methods, supported by widely documented successful results.

Backup for GPS, strongly urged in the widely acclaimed 2001 Volpe report, remains incomplete. Continuation of this condition calls to mind the Titanic or the 2008 financial fiasco. Meanwhile, shortcomings of GPS integrity tests are described and inescapably demonstrated by citing a document from the spring of 2000, plus history of flightworthiness improperly bestowed with proprietary rights accepted for algorithms and tests (rather than rigor advocated two decades ago ; #57 of the publication list ). A subsequently documented panel discussion shows the extent of unpreparedness in the legal realm.

While bending over backwards to acknowledge that disaster is unlikely, an unflinching look reviews potential though improbable consequences. The meaning of G in GPS suggests that “unlikely” isn’t enough.

Although this is old information, realization has not been widespread. Also, present plans for upgrading to Automatic Dependent Surveillance Broadcast (ADSB) raise new concerns (#83 of the publication list , plus various blogs on this site related to collision avoidance, runway incursions, … ). This dialogue is prompted by considerations of safety. Again, “low” likelihood combined with absence of a calamity thus far offers no guarantee. I advocate a revisit of this issue with all its ramifications.

Genesis of Flight Performance Requirements

Wed, 17 Jul 2013 02:13:00 GMT

An intense discussion among LinkedIn UAV group members involves several important topics, including the source of a one-out-of-a-billion requirement for probability of a mishap. The source is thus far unidentified.

I can shed some light on the genesis of another related requirement. From within RTCA SC-195 (GPS Integrity) Working Group for FDI/FDE (Fault Detection and Isolation / Fault Detection and Exclusion) in the 1990s, parameters were used to establish the Missed Detection requirement as follows:
* From records obtained as far back as possible (1959) there were over 333 million flight-hours nationwide between 1959 and 1990.
* In the (inevitably imperfect) real-world, the maximum allowable number of hull-loss accidents in 30 years cannot be specified at zero; so that maximum allowable number was set to one, producing 3 billionths per flight-hour
* The number used for mean time between loss of GPS integrity was 18 years.
* Probability of an unannounced SV (satellite) malfunction is then 1 – exp{ -1/18x365x24 } = approx. 6 millionths per hr per SV.
* Since 6 SVs are needed for FDE, that probability is multiplied by 6, producing 36 millionths per hour as the probability of an unannounced SV malfunction in any SV among those chosen for FDE.
* Probability of an undetected unannounced SV malfunction is then 36 millionths per hour multiplied by Missed Detection probability.
* With an incident/accident ratio slightly below 1/10, a value of 0.001 for Missed Detection probability satisfies the 3 billionths per flight-hour requirement.

None of this is intended to signify thoroughness in the genesis of decisions affecting flight safety requirements. Neither demands for rigorous validation in early 1994, nor an attempt to facilitate meeting those demands — via replacement of GO/No-GO testing by quantitative assessment — met the “collective-will” acceptance criteria. History related to that, not reassuring, is recounted on page 5 of a synopsis offered here and page 127 of GNSS Aided Navigation & Tracking . The references just cited, combined with additional references within them, address a challenging topic: how to substantiate, with high confidence, satisfaction of very low probabilities. There are methods, using probability scaling, not yet accepted.

Returning to the original question that prompted this blog: It might be uncovered — possibly from some remote source — that the number with a mysterious origin was supported, at one time, by some comparable logic.

Elmen C. Quesinberry

Mon, 15 Jul 2013 01:21:00 GMT

Earlier this year I wrote a belated tribute to a well-known pioneer in strapdown . Now I must write another tribute, even more belated, to a pioneer who was less well-known — but with a legacy equal to any other whose work helped mine to come alive.

Over three decades (Feb 1961 to Nov 1993) I was a full-time employee of Westinghouse (division names varied from AirArm to DESC to …) — but what I want to express here is first of all a salute to many of the people whose paths crossed with mine. That word “many” is no exaggeration; one recollection that stands out occurred during a chance conversation with Tim Gunn, at about lunch hour, near the cafeteria. Over and over again, seemingly everyone-&-their-brother walking by, was saying “Hi” to me. Tim was flabbergasted at how many people I knew, whether they were from the shop (in some of those cases, from barbershop quartet or other music activities, sports, ... ) or — in many other cases — from one department or another of engineering.

In recollection it is crystal clear that, during that time period, I was privileged to work with many of the best. That includes names like Joe Dorman, Jim Mims, … And when position/velocity/acceleration gains had to be set for track at lock-on over 7 octaves of range with 16-bit words, George Axelby and John Stuelpnagel helped show the way — and who could forget the Schafer/Leedom/Weigle triumvirate or, from TIR, Bill Hopwood or, from software, names like Heasley + Landry + Kahn + Clark (who as a techie was among the best, as was another from his group — working with me on A12 when John crossed into management) — plus others, too numerous to mention. Many of the latter names are more obscure, it is realized; in some ways that’s the most important part of this effort, to give credit where credit is overdue. One of the best program manners was named Willett, again not among the most famous within Westinghouse. Of all the best-and-brightest named &/or unnamed here though, no one stands higher in my memory than Elmen C. Quesinberry. His contribution to Westinghouse’s collection of achievements over time is realized by only very few. I guess what’s important is that he realized it himself; he earned every bit of his salary, and much more.

This revisit-of-history isn’t intended to imply that all was sunshine + roses; in fact, we encountered much major opposition. No need to go into detail here, but many had peripheral (or less) understanding. I made my peace with those long ago and have no desire to retract it. For doubters, flight-validated results appear elsewhere on this site. Enough said; of central importance here is the lasting legacy of a truly great engineer. Elmen C. Quesinberry, a true Christian gentlemen, was an outstanding engineer whose collaboration gave me benefits unsurpassed by any other over three decades at Westinghouse.

NOW IT’S ALL FLIGHT-VALIDATED (The Case Builds)

Fri, 21 Jun 2013 21:00:00 GMT

In 2013 a phone presentation was arranged, for me to talk for an hour with a couple dozen engineers at Raytheon. The original plan was to scrutinize the many facets and ramifications of timing in avionics. The scope expanded about halfway through, to include topics of interest to any participant. I was gratified when others raised issues that have been of major concern to me for years (in some cases, even decades). Receiving a reminder from another professional, that I’m not alone in these concerns, prompts me to reiterate at least some aspects of the ongoing struggle — but this time citing a recent report of flight test verification .

The breadth of the struggle is breath taking . The About panel of this site offers short summaries, all confirmed by authoritative sources cited therein, describing the impact on each of four areas (satnav + air safety + DoD + workforce preparation). Shortcomings in all four areas are made more severe by continuation of outdated methods, as unnecessary as they are fundamental, Not everyone wants to hear this but it’s self-evident: conformance to custom — using decades-old design concepts (e.g., TCAS) plus procedures (e.g., position reports) and conventions (e.g., interface standards — guarantees outmoded legacy systems. Again, while my writings on this site and elsewhere — advocating a different direction — go back decades, I’m clearly not alone (e.g., recall those authoritative sources just noted). Changing more minds, a few at a time, can eventually lead to correction of shortcomings in operation.

We’re not pondering minor improvements, but dramatic ones. To realize them, don’t communicate with massaged data; put raw data on the interface. Communicate in terms of measurements, not coordinates — that’s how DGPS became stunningly successful . Even while using all the best available protection against interference, (including anti-spoof capability ), follow through and maximize your design for robustness ; expect occurrences of poor GDOP &/or less than a full set of SVs instantaneously visible. Often that occurrence doesn’t really constitute loss of satnav; when it’s accompanied by history of 1-sec changes in carrier phase , those high-accuracy measurements prevent buildup of position error. With 1-sec carrier phase changes coming in, the dynamics don’t veer toward any one consistent direction; only location veers during position data deficiencies (poor GDOP &/or incomplete fixes) and, even then, only within limits allowed by that continued accurate dynamic updating. Integrity checks also continue throughout .

So then, take into account the crucial importance of precise dynamic information when a full position fix isn’t instantaneously available. Take what’s there and stop discarding it. Redefine requirements to enable what ancient mariners did suboptimally for many centuries — and we’ve done optimally for over a half-century. Covariances combined with monitored residuals can indicate quality in real time. Aircraft separation means maintaining a stipulated relative distance between them, irrespective of their absolute positions and errors in their absolute positions. None of this is either mysterious or proprietary, and none of this imposes demands for huge budgets or scientific breakthroughs — not even corrections from ground stations.

A compelling case arises from cumulative weight of all these considerations. Parts of the industry have begun to address it. Ohio University has done flight testing (mentioned in the opening paragraph here) that validates the concepts just summarized. Other investigations are likely to result from recent testing of ADSB. No claim is intended that all questions have been answered, but — clearly — enough has been raised to warrant a dialogue with those making decisions affecting the long term.

INFRASTRUCTURE

Sun, 09 Jun 2013 19:33:00 GMT

The sky isn’t falling but some of our bridges are. About seventy thousand of them are structurally deficient, and about a quarter of those could go at any time. Calamities are sure to mount if nothing is done. The number that will occur (e.g., after belated prevention efforts) is unknown.

That number could be reduced by a method not currently in use. In combination with other steps (placement of sensors at strategic locations on a structure) a historical pattern of deformations can be generated automatically. The means of analyzing the deformations has already been shown to provide early warning capability, via application to data recorded before the 2011 Tohoku earthquake. There is no need to repeat the description here; it’s already documented .

Sooner or later another subject comes up: The “C” word (cost). Aside from severity of the problem, about the only other item prompting agreement is the notion that a solution is unaffordable. Let me change that notion this way: if a complete solution is deemed unaffordable, a partial solution doesn’t have to be. Prioritize . Bridges exhibiting the most urgent warning signs are highest priority for remedial action. At 1/70,000th of the total cost, no one could reasonably refuse to fix one that must be fixed.

An acknowledgment: the argument just cited is overstated. Initial investment is always a greater fraction of the long-term total, and applying a method for the first time to any operation requires ironing out some wrinkles. Still, admitting that a fraction exceeds 1/70,000 doesn’t constitute a shocking confession. The sensors don’t have to be top-of-the-line. If the “bottom line” is all that matters, then here’s the real bottom line: Their cost, plus the cost of a government-sponsored project, pales in comparison with losses resulting from a bridge collapse — let alone the losses incurred from seventy thousand collapsed bridges.

John Bortz

Sun, 02 Jun 2013 21:11:00 GMT

In February of this year the navigation community lost a major contributor to navigation -- John Bortz. To many his name is best known in connection with "the Bortz equation" which easily deserves a note here to highlight its significance in development of strapdown inertial nav. Before his work in the early 1970s, strapdown was widely considered as something with possible promise "maybe, if only it could ever come out of the lab-&-theory realm" and into operation. Technological capabilities we take for granted today were far less advanced then; among the many state-of-the-art limitations of

that time, processing speed is a glaringly obvious example. To make a long story short, John Bortz made it all happen anyway. Applying the previously mentioned equation (outgrowth of an early investigation of Draper Lab's Dr. J.H. Laning) was only part of his achievement. Working with 1960s hardware and those old computers, he made a historic mark in the annals of strapdown. Still, importance of that accomplishment should not obscure his other credentials. For example, he also made significant contributions to radio navigation -- and he spent the lst two decades of his life as a deacon.

1-sec Carrier Phase (again)

Sun, 05 May 2013 04:40:00 GMT

A comment challenged my video . I’m glad it included an acknowledgment that some points might have been missed. To be frank that happened a bunch; bear with me while I explain. First, there’s the accuracy issue; doppler &/or deltarange info provided from many receivers is far less accurate than carrier phase (sometimes due to cutting corners in implementation — recall that carrier phase, as the integral of doppler, will be smoother i f processing is done carefully). Next, preference for 20-msec intervals will backfire badly. If phase noise at L-band gives a respectable 7mm = 0.7cm, doppler velocity error [(current phase) – (previous phase)] / 1 sec is (1.414) (0.7) = 1 cm/sec RMS for a 1-sec sequential differencing interval. Now use 20 msec: FIFTY times as much doppler error! Alternatively if division is implicit instead of overt, degradation is more complicated: sequential phase differences are highly correlated (with a correlation coefficient of -1/2, to be precise). That’s because the difference (current phase) – (previous phase) and the difference (next phase) – (current phase) both contain the common value of current phase. In a modern estimation algorithm, observations with sequentially correlated errors are far more difficult to process optimally. That topic is a very deep one; Section 5.6 and Addendum 5.B of my 2007 book address it thoroughly. I’m not expecting everyone to go through all that but, to offer fortification for its credibility, let me cite a few items:

* agreement from other designers who abandoned efforts to use short intervals
* table near the bottom of a page on this site .

* phase residual plots from Chapter 8 of my 2007 book.

The latter two, it is recalled, came from flight test for an extended duration (until flight recorder was full), under severe test aircraft (DC-3) vibration.

For doppler updating from sources other than satnav, my point is stronger still. Doppler from radar (which lacks the advantage of passive operation) won’t get velocity error much below a meter/sec — and even that is an improvement over unaided inertial nav (we won’t see INS velocity specs expressed in cm/sec within our lifetime).

Additional advantages of what the video offers include (a) no requirement for a mask angle, (b) GNSS interoperability, and (c) robustness. A brief explanation:

(1) Virtually the whole world discards all measurements from low-elevation satellites because of propagation errors. But ionospheric and tropospheric effects change very little over a second; 1-sec phase differences are great for velocity information. Furthermore they offer a major geometry advantage while occurrence of multipath would stick out like a sore thumb, easily edited out .
(2) 1-sec differences from various constellations are much easier to mix than the phases themselves.
(3) For receivers exploiting FFT capability even short fragments of data, not sufficiently continuous for conventional mechanizations (track loops), are made available for discrete updates.
The whole “big picture” is a major improvement is robust operation

The challenger isn’t the only one who missed these points; much of our industry, in fact, is missing the boat in crucial areas. Again I understand skepticism, but consider the “conventional wisdom” regarding ADSB: Velocity errors expressed in meters per second — you can hear speculative values as high as ten . GRADE SCHOOL ARITHMETIC shows how scary that is; collision avoidance extrapolates ahead. Consider the vast error volume resulting from doing that 90 seconds ahead of closest approach time with several meters per second of velocity error. So — rely on see-and-avoid? There are beaucoup videos that show how futile that is (and many more videos that show how often near misses occur — in addition there are about a thousand runway incursions each year). That justifies the effort for dramatic reduction of errors in tracking dynamics — to cm/sec relative velocity accuracy.

It’s perfectly logical for people to question my claims if they seem too good to be true. All I ask is follow through, with visits to URLs cited here.

Avionics Commonality

Mon, 25 Mar 2013 22:11:00 GMT

A LinkedIn discussion centered on the Future Airborne Capability Environment (FACE) standard contained an important observation concerning certification. Granted — requirements for validation, with acceptance by governing agencies, definitely are essential for safety. What follows here is advocacy for a proposed way to realize the common avionics benefits offered by FACE while retaining (and in fact, improving) the process of certification. Reasoning is based on three major items:

* CHANGE. In many respects this has necessitated improved standards.

* HISTORY. Spectacular failures in what we have now are widely documented.

* COST. The status quo is (and, for a long time, has been) unaffordable.

In regard to the first item: the pace of change in so many areas (hardware, software, operating systems, data communication, etc., etc., etc.) — and the effects on procurement cycles — are well known. How can certification remain unchanged when nothing else does? That argument would be undercut if the process had a rock solid track record — but that theme would not be supported by the second item — history:

Myriad shortcomings of existing operational systems are so pervasive that no one is considered a “loose cannon” for openly discussing them. Any of my horror stories — too strange and too numerous to be revisited here — would be trumped anyway by a document from the government itself. GAO-08-467SP, in 2008, described outlandish cost overruns, schedule delays, and deficient technical performance in the defense industry. That 3-way combination speaks for itself. Now a significant addition: the certification process has not been at all immune to serious flaws. The first-ever certified GPS receiver is now well known to have failed spectacularly in multiple facets of integrity testing by another manufacturer. It is readily acknowledged that correction of those early problems is quite credible, but one issue is inescapable: Historical proof of flightworthiness improperly bestowed — with proprietary rights accepted for algorithms and tests –- happened , and that was not widely known until much later.

There is still more, including integrity failure probability limits missed by orders-of-magnitude in certified GPS receivers, severe limitations of GO/NO-GO testing, and failed attempts to gain approval to set requirements for correcting those plus other deficiencies. For brevity here, those issues are covered by citing the fifth page from another related reference .

The final item is, after years of fruitless talk about cost reduction, being acknowledged — we can’t do what we’ve been doing any more. With dollars being the ultimate driver of so many decisions, we might finally see the necessary break from ingrained habits. FACE already addresses the issues and the requisite justifications. To make it all happen, two essential ingredients are

* raw-data-across-the-board, and * nonproprietary software, with standardization under government control.

Flight-validated algorithms already in existence can be converted (e.g., from proof-of-concept to in-flight real-time form) according to government specification, by small groups more interested in engineering than in dollars (yes, that does exist). The payoff in cost savings can be huge.

Open System Architecture for Radar

Tue, 19 Mar 2013 02:48:00 GMT

Significant momentum is evolving toward a role for Open System Architecture (OSA) applied to radar . My observations in connection with that, voiced in a short LinkedIn discussion, seem worth repeating here.

One step could add major impact to this development: Rather than position (or relative position) outputs, provide measured range, azimuth, elevation (doppler could optionally be added if applicable) on the output interface. That simple step would vastly improve effectiveness of track file maintenance. Before attempting to describe all reasons for improved performance, two obvious benefits can be identified first:
* ability to use partial information (e.g., range-only or, for passive operation, angle-only)
* proper weighting of data for updating track state estimates.
The first item is self-evident. The second arises from common-sense attachment of greater value to the most accurate information. An explanation:

One-sigma error ellipsoids for individual radar fixes are not spherical (not a beachball shape but more like a flattened beachball), even at close range. At longer distances the shape progresses from a frisbee to a pancake to a DVD. Kalman filtering has enabled us to capitalize on that feature for over a half-century. Without exploiting it, we effectively treat separate radar-derived “coordinates” by intersecting volumes in space that are common to overlapping spheres. Resulting uncertainty volume is enormously larger than it should be.

The feature just noted shows up dramatically when mixing data among multiple platforms. Consider cooperative engagement whereby participants, all tracking each other via network-transmitted GPS observations, share radar observations from an unknown non-participant. Share measurements or coordinates? No contest; multiple lines crossing from different directions can offer best (i.e., along-range) accuracies applicable in 3-D.

That fact (i.e., combining data from different sensors and different platforms further dramatizes available improvements) doesn’t diminish the basic issue; even with a time history of data from only one radar, a designer with direct measurements available — instead of, not in addition to, coordinates — can provide incomparably superior performance.

“ Send Measurements not Coordinates ” (1999; #66 from the “Published Articles” panel, opening with eight rock-solid reasons) was aimed at GPS rather than radar. Many of the principles are the same when mixing data with information from other platforms — and from other sensors such as GPS. There is no reason, in fact, why data from satellite navigation and radar can’t be combined in the same estimation algorithm. That practice hasn’t evolved but the historical separation of operations (e.g., navigation and surveillance), arising from old equipment limitations, should no longer be a constraint. Moreover, with focus shifted from tracking to navigation, integration with additional (e.g., inertial) data offers still more reasons for using direct measurements. Rather than loose integration, superior benefits are widely known to result as the sophistication progresses forward (tight. ultratight, and deep integration).

Further elaborations on “casting off our old habits” appear from different perspectives in various blogs, one-pagers, and a few manuscripts available at this site. If your library has a copy of GNSS Aided Navigation & Tracking pages 203-4 show a way to implement the cooperative sharing of radar data obtained from a non-participant, among participants tracking each other via the mutual surveillance and tracking approach defined earlier in that same chapter.

Because so many operational systems (in fact, a vast majority) use reports in the form of coordinates, reiteration is warranted. The central issue is the content , not the amount, of data. Rather than coordinates, provide accurately time-stamped direct measurements with links connected to whichever platform observed the data (e.g., for satnav — pseudoranges; for radar — range, azimuth, elevation). Those links are automatically attached when Mode-S extended squiter (e.g., chosen for ADSB) is the means for conveying the data. For message content , strictly disallow “massaging the data beyond the light of day” (e.g., by unknown processes, with uncertain timing, … ) which invariably results in enormous loss of performance in common occurrence today.

CONING in STRAPDOWN SYSTEMS

Mon, 03 Sep 2012 22:00:00 GMT

Free-inertial navigation uses accelerometers and gyros alone, unaided. For that purpose pioneers of yesteryear developed a variety of techniques, ranging from a 2-sample approach (NASA TND-5384, 1969) by Jordan to his and various others’ higher-order algorithms to reduce errors from noncommutativity of finite rotations in the presence of coning ( and / or pseudo coning). The methods showed considerable insight and produced successful operation. Since it’s always good to have “another tool in the toolbox” I’ll mention here an alternative. What I describe here isn’t being used but, with today’s processing capabilities, could finally become practical. The explanation will require some background information; I’ll try to be brief.

A very old investigation (“Performance of Strapdown Inertial Attitude Reference Systems,” AIAA Journal of Spacecraft and Rockets, Sept 1966, pp 1340-1347) used the usual small-angle representation for attitude error expressed in the vehicle frame. With that frame rotating at a rate omega the derivative of that vector therefore contains a cross product of itself crossed with omega . One contributor to that product is a lag effect from omega premultiplied by a diagonal matrix consisting of delays (e.g., transport lags equated to reciprocals of gyro bandwidths). Mismatch among those diagonal elements produces drift components with nonzero average, e.g., the x-component of the cross product is easily seen to be
(difference between y and z lags) times (omega_y) times (omega_z).
Even with zero-average (e.g., oscillatory) angular rates, that product has nonzero average due to rectification. I then characterized the lags as delays from computation rather than from the gyros, with the lag differences now proportional to nonuniformities among RMS angular rate components along vehicle axes, and average products proportional to cross-correlation coefficients of the angular rate components. That was easy; I had a simple model enabling me to calculate the error due to finite gyro sampling rates producing finite rotation increments that don’t commute.

A theoretical model is only that until it is validated. I had to come up with a validation method with mid-1960s computational limitations. Solution came from a basic realization: performance doesn’t degrade from what’s happening but from belief in occurrences that aren’t happening. The first-ever report of coning (Goodman and Robinson, ASME Trans, June 1958) came from a gimballed platform that was believed to be stable while it was actually coning. If the true coning motion they described had been known and taken into account, then their high drift rates never would have occurred. The reason they weren’t taken into account then was narrow gimbal servo bandwidth; the gyros responded to the coning frequency but the platform servos didn’t. Now consider strapdown with the inverse problem: pseudo coning — a vehicle believed to experience coning when it isn’t. That will fall victim to the same departure of perception from reality. If you gave the same Goodman and Robinson coning motion to their strapdown gyro triad and sampled them every nanosecond, the effect from noncommutativity wouldn’t be noticeable.

Armed with that insight I then chose rotational dynamics with a closed form solution. Although rotations about fixed vehicle axes produced no coning, the pseudoconing was severe, with the apparent (reported-from-gyros) rotation axis changing radically within fractions of a millisecond; too fast for the 10 kHz data rate used in that computation. The cross product formulation was then validated by making extensive sets of runs, always comparing two time histories:

* a closed form solution for a true direction cosine matrix corresponding to a vehicle experiencing a sinusoidal omega
* an apparent direction cosine matrix, obtained by brute-force but meticulous formation from processing gyro outputs at finite rates with quantization, time lags, and a wide variety of error sources.

That “bull-by-the-horns” computation allowed extended runs (up to a million attitude iterations) to be made for a wide range of angular rate frequencies, axis directions, and combinations of gyro input errors (steady, random, motion-sensitive, etc.). Deviation of apparent attitude from closed-form truth was consistently in close conformance to the analytical model, for a host of error sources. I have to admit that this “bull-by-the-horns” approach gave me an advantage of finding out answers before I understood the reasons for them. The cross-product analytical model didn’t come from my vision; it came after much head-scratching with answers computed from dozens of runs. A breakthrough came from the sensitivity, completely unanticipated, to angular acceleration about gyro output axes — clear in retrospect but not initially. After these experiences it occurred to me: if cross-axis covariances were known, the dominant contributor to errors — including noncommutativity — could be counteracted. I noted that on page 1342 of that old AIAA paper.

Finally I can describe the alternative means of compensating the dominant computational error. Description begins with the reason why it would be useful. Earlier I mentioned that many authors developed very good algorithms to reduce errors from noncommutativity of finite rotations in the presence of coning and/or pseudoconing. All that history, plus more detailed presentation of everything discussed here, can be found in Chapters 3 and 4 of my 1976 book plus Addendum 7.A of my 2007 book. A supreme irony upstages much of the work from those brilliant authors: without accounting for gyro frequency response characteristics, the intended benefit can be lost — or the “compensation” can even become counterproductive (Mark and Tazartes, AIAA Journal of Guidance, Control, & Dynamics, Jul-Aug 2006, pp 641-647). As if those burdens weren’t enough, the adjustment’s complexity — as shown in that paper — can be extensive. So : that motivates usage of a simpler procedure.

By now I’ve put so much explanation into preparing its description that not much more is needed to define the method. Today’s signal-processing boards enable the requisite covariances to be repetitively computed. Then just form the vector cross product already described and subtract the result from the gyro increments ahead of attitude updating. So much for coning and pseudoconing — but I’m not quite finished yet. The paper just cited leads to another consideration: even if we successfully removed all of the error theoretically arising from inexact computation, significant improvement in free-inertial performance would require more. Operation in the presence of vibrations would necessitate reduction of other motion-sensitive errors. Gyro degradations from rotations, for example, would have to be compensated — and that includes a multitude of components. For that topic you can begin with the discussion of gyro mounting misalignment following that up with the tables in Chapter 4 of my 1976 book and Addendum 4.B of my 2007 book.

LORAN REVISITED

Sun, 10 Jun 2012 02:15:00 GMT

Now that several years have passed since the LORAN-C budget was killed, it might be a good time to revisit that decision. Unlike other decisions, this was partially undone; despite the inexcusable demolition of many resources (e.g., towers, transmitters) a few sites were spared, and cooperative effort between the Coast Guard and UrsaNav Inc. procuced successful results. More recently, congressional action authorized establishment of a terrestrial backup timing system for GPS by 2020.

For brevity here it suffices to make a few surface-scratching notes. The vast majority of us in the navigation community recognized the potential benefit of LORAN (and an extended form eLORAN) as a crucial backup — at extremely low cost — to be used when GPS is unavailable. Many of us, furthermore, anxiously pressed for sanity (e.g., my “2-cents worth” written, to no avail, in 2009).

What’s different now, conceivably, is a combined effect of multiple factors:
* The USCG/UrsaNav success surpassed goals that had been stated earlier.
* Awareness of GPS vulnerability (therefore need for backup) has increased considerably with repeated instances of GPS jamming in both maritime and airborne operations.
* Persistent efforts by the RNT Foundation and others have resulted in Congressional action.

An utterance appearing in Coordinates Magazine’s March 2012 cover story was reached from a different context, but its importance prompted me to cite it in the April 2012 cover story — and to repeat it here: “Do we really need to wait for a catastrophe before taking action against GNSS vulnerabilities?”

Once again I’m adding my voice to the chorus of those speaking out before it’s too late.

James L. Farrell featured in April 2012 Cover Story of Coordinates Magazine

Sun, 20 May 2012 19:09:00 GMT

Click the image to view the full article now!

Resume for James L. Farrell, PHD

Sun, 20 May 2012 18:21:00 GMT

I perform functional formulations and algorithm generation plus validation for both simulation and operational purposes in system integration. Specific areas include navigation, communication, data integrity, and tracking for aerospace, applying modern estimation to data from various sources (COMM, gyros, accelerometers, GPS/GNSS, radar, optical, etc.).

Complete Viewable & printable Resume Click Here … (opens in new window)

Dept. of Homeland Security on GPS jamming & spoofing

Fri, 09 Sep 2011 18:53:00 GMT

At ION GNSS 2011 in Portland OR, Javad Ashjaee, James L. Farrell and others participated in a panel discussing the U.S. Dept. of Homeland Security’s concerns on the effects of GPS jamming and spoofing on our national critical infrastructure.

As Dr. Todd Humphreys noted, U.S. Dept. of Homeland Security recently completed a risk assessment of the effects of GPS jamming and spoofing on national critical infrastructure. Some of us participated as subject matter experts in this assessment.

The DHS report, which is the most thorough one to date on this topic, has left many people saying “Yes, it’s a problem. Now what?”

This panel addressed the question “Now what?”

Topic: How do we secure civil GNSS?

Schedule

ION GNSS 2011

September 19-23, 2011 (Tutorials: September 19-20)
Oregon Convention Center, Portland, Oregon

POST-CONFERENCE UPDATE

A subsequent experiment conducted in Texas, attracting national attention at that time, became the topic of eMail communications among several professionals in the satnav community. That sequence of communications resulted in a summary published in GPSWorld .

Life before GPS

Fri, 02 Sep 2011 21:39:00 GMT

Before GPS took over so many operations by storm (e.g., navigation,tracking, timing, surveying, etc.), designers had access to other — far less capable — provisions. That condition forced our hands; to derive maximum benefit from what was available, we had to extract full information content from those provisions. Now that GPS is subjected to challenges (aging, jamming, spoofing , etc.), some of those older methods are receiving increased scrutiny. Recently I’ve received renewed interest in areas I analyzed decades ago. Old publications from two of those areas are discussed here: 1) attitude determination and 2) nav integration.

“Attitude Determination by Kalman Filtering” is the title of three documents I had published. In reverse sequence they are:
1) Automatica (IFAC Journal), v6 1970, pp. 419-430,
2) my Ph.D. dissertation (Univ. of Maryland, 1967),
3) NASA CR-598, Sept., 1966.
As indicated by the last reference, the work was the result of a contractual study sponsored by NASA (specifically Goddard Space Flight Center – GSFC – in Greenbelt Maryland). I was working for Wetinghouse Defense and Space Center at the time. The proposal I had written to win this contract cited my work prior to then, in both modern estimation (“Simulation of a Minimum Variance OrbitalNavigation System,” AIAA JSR v 3 Jan 1966 pp. 91-98) and attitude computation (“Performance of Strapdown Inertial Attitude Reference Systems,” AIAA JSR v 3 Sept 1966, pp. 1340-1347). Let me hasten to explain the dates of those Journal publications: each followed its inclusion at an AIAA-sponsored conference, about a year earlier.

By the mid-1960s there was an appreciable amount of validation for Kalmen filtering applied to determination of orbits (that track record was convincing) but not yet for attitude. A GSFC-sponsored investigation was then planned — the very first one for attitude using modern estimation methods as acknowledged in Fundamentals of Spacecraft Attitude Determination and Control Chapter 1. GSFC management understandably wanted that contractual investigation to be performed by someone with demonstrable experience in both Kalman filtering and rotational dynamics. In those days that combination was rare; the Westinghouse proposal was chosen as the winner. At the time of that study, provisions realistically available for attitude updating consisted of mediocre-accuracy items such as magnetometers and horizon scanners– not bad but not spectacular either.
All that was of course before GPS weighed in, with its opportunity to reveal attitude from phase differences between antennas spaced at known distances apart. That vastly superior capability effectively reduced earlier crude measurements to relative obscurity. A directly parallel situation occurred in connection with navigation; the book that first tied together several facets of advancement in that field (integration, strapdown inertial, modern estimation with acceptance of all data sources, multimode operation, extension to tracking, clear exposition of all commonly used representations of attitude, etc.) was”pre-GPS” (1976), and consequently regarded as less relevant. Timing can be decisive — that’s no one’s fault.

The item just noted — attitude representation — is worth further discussion here. Unlike many other sources, my 1976 book offered an opportunity to use quaternion properties without any need to learn a specialized quaternion algebra. A literature search, however, will point primarily to various sources (of necessity, later than 1976).that benefit from the superior performance offered through GPS usage. Again, in view of GPS as a game-changer, that is not necessarily improper. Most publications on attitude determination don’t cite the first-ever investigation, sponsored by GSFC, for that innocent reason.

The word beginning that last sentence (“Most”) has an exception. One author, widely quoted as an authority (especially on quaternions), did cite the original work — dismissing it as “ad-hoc” — while using an exact copy of the sensitivity matrix elements pubished in my original investigation (the three references cited at the start of this blog).
Obviously I didn’t invent either quaternions or the Kalman filter. Unlike the author just mentioned, also, I didn’t fail to credit, in my publications, pre-existing sources that contributed to my findings. Publication of the material cited here, I’ve been told, paved the way for understanding and insight to many who followed. No one owes me anything for that; an analyst’s work, truthfully and realistically presented, is what the analyst has to offer.

It is worth pointing out that both the attitude determination study and the 1976 book cover another facet of rotational analysis absent from many other related publications: dynamics — in the sense of physics. Whereas modern estimation lumps time-variations of the state together into one all-encompassing “dynamic” model, classical physics makes a separation: Kinematics defines the relation between position, rates, and accelerations. Dynamics determines translational accelerations resulting from forces or rotational accelerations resulting from torques.

Despite absence of GPS from my early (1960s/70s) investigations, one feature that can still make them useful for today’s analysts is the detailed characterization of torques acting — in very different ways — on spinning and gravity-gradient satellites, plus their effects on rotational motion. Many of the later studies focused on the rotational kinematics, irrespective of those torques and their consequences. Similarly, the “minimal-math”approach to explaining integrated navigation has enabled many to grasp the concepts. Testimony to that is contained in the above citation of my 1976 book .

RUNWAY INCURSIONS

Mon, 20 Jun 2011 02:51:00 GMT

The number of runway incursions, as shown on an FAA URL was nearly a thousand in FY 2011 and 1150 for FY 2012. Aviation-related blogs show renewed interest in their prevention.

A huge reduction in velocity error (from meters/sec to cm/sec) was shown in flight for squitter message transmission — but with measurement-based message content, as discussed in a publication describing dramatic success in air (3-D), easily extendable to 2-D (surface).

BOOK on TRACKING

Sun, 06 Mar 2011 01:20:00 GMT

Tracking acceleration dynamics by GNSS, radar, imaging

In addition to the flight-validated algorithms for navigation (processing of inertial sensor data, integration with GPS/GNSS , integrity, etc.) my 2007 book , as its title implies, offers extensive coverage of tracking . The longest chapter of the book (Chapter 9) provides formulations for a variety of modes, in 2-D (e.g., for runway incursion prevention or ships) and 3-D (in-air), using GPS/GNSS and/or other sensors (e.g., radar , optical). Position and velocity vectors are formed, in some operations joined by some or all components of acceleration .

This author was “at-the-right-places at-the-right-times” when a need arose to address each of the topics covered. As a result, the words of one reviewer — that the book is “ teeming with insights that are hard to find or unavailable elsewhere ”

applies to tracking as well as to navigation. The book identifies subtleties that arise in specific applications ( aircraft , ships, land vehicles, satellites, long-range or short-range projectiles , reentry vehicles, missiles , … ). In combination with a variety of possible conditions affecting sensor suite and location (air-to-air; air-to-ground; air-to-sea surface; surface-to-air, etc. — with measurements associated with distance or direction or both; shared or not shared among participants who may communicate from different positions), it is not surprising that striking contrasts can arise, influencing approaches and characterizations used. The array of formulations offered, while fully accounting for marked differences among operations, nevertheless exploits an underlying commonality to the maximum possible extent.

Tracking dynamics of aircraft, missiles, ships, satellites, projectiles, …

Formulations described in Chapter 9 were used for tracking of both aircraft and missiles , concurrently, through usage of an agile beam radar . For another example, air-to-surface operations subdivide into air-to-ground and vessel tracking from the air. That latter case constrains tracked objects’ altitudes to mean sea level — a substantial benefit since it obviates the need for elevation measurements, which are subject to large errors from refraction (bearing and range measurements, much less severely degraded, suffice). Air-to-ground tracking , by contrast, further subdivides into stationary and moving targets; the former potentially involves imaging possibilities (by real or synthetic aperture) while the latter — if not being imaged by inverse SAR — separates its signature from clutter via doppler.

Reentry vehicles, quite different from other track operations, present a unique set of “do’s” and “don’ts” owing to high-precision range measurements combined with much larger cross-range errors (because of proportionality to extreme distances involved). Pitfalls from uncertain axial direction of “pancake” shaped one-sigma error ellipsoids must be avoided. A counterexample, having angle observations only (without distance measurements), is also addressed. Orbit determination is unique in still another way, often permitting “patched-conic” modeling for its dynamics . A program based on Lambert’s theorem provides initial trajectories from two position vectors with the time interval separating them.

Those operations and more are addressed with most observations from radar or other (e.g., infrared imaging) sensors rather than satellite measurements. That of course applies to tracked objects carrying no squitters. Friendlies tracking one another, however, open the door for using GNSS data. Those subjects plus numerous supporting functions are discussed at some length in Chapter 9. Despite very different dynamics applicable to various operations, the underlying commonality (Chapter 2) connects the error propagation traits in their estimation algorithms and also — though widely unrecognized — short-term INS error propagation under cruise conditions (Chapters 2 and 5). Support operations such as synthetic aperture radar ( SAR ) and transfer alignment are described in the chapter Addendum.

Book on GPS and GNSS

Sat, 26 Feb 2011 20:45:00 GMT

GPS and GNSS

Check out a preview of “GNSS Aided Navigation & Tracking” ( click here )

– Inertially Augmented or Autonomous
By James L. Farrell
American Literary Press. 2007. Hardcover. 280 pages
I SBN-13: 978-1-56167-979-9

This text offers concise guidance on integrating inertial sensors with GPS and also its international version (global navigation satellite system; GNSS ) receivers plus other aiding sources. Primary focus is on low-cost inertial measurement units (IMUs) with frequent updates, but other functions (e.g., tracking in numerous modes) and sensors (e.g., radar) are also addressed.

Price is: $100.00 Plus Shipping(Sales Tax for Maryland residents only)

Dr. Farrell has many decades of experience in this subject area; in the words of one reviewer, the book is “teeming with insights that are hard to find or unavailable elsewhere.”

Farrell has made a number of contributions to multiple facets of navigation. He is also the author of Integrated Aircraft Navigation (1976; five hard cover printings; now in paperback) plus over eighty journal or conference manuscripts and various columns.

Frequent aiding-source updates, in applications that require precise velocity rather than extreme precision in position, enables integration to be simplified. All aspects of integration are covered, all the way from raw measurement pre-processing to final 3-D position/velocity/attitude, with far more thorough backup and integrity provisions. Extensive experimental results illustrate the attainable accuracies (cm/s RMS velocities in three-dimensions) during flight under extreme vibration.

The book on GPS and GNSS provides several flight-validated formulations and algorithms not currently in use because of their originality. Considerable opportunity is therefore offered in multiple areas including
* full use of highly intermittent ambiguous carrier phase
* rigorous integrity for separate SVs
* unprecedented robustness and situation awareness
* high performance from low cost IMUs
* “cookbook” steps
* new interoperability features
* new insights for easier implementation.

Discussion of these traits can be seen in the excerpt (over 100 pages) from the link at the top of this page.

GYRO MOUNTING MISALIGNMENT: DEAL BREAKER

Fri, 15 Oct 2010 03:01:00 GMT

Schuler cycles distorted — Here’s why

A 1999 publication I coauthored took dead aim at a characteristic that received far too little attention — and still continues to be widely overlooked: mechanical mounting misalignment of inertial instruments. To make the point as clearly as possible I focused exclusively on gyro misalignment — e.g., the sensitive axes of roll, pitch, and yaw gyros aren’t quite perpendicular to one another. It was easily shown that the effect in free-inertial coast (i.e., with no updates from GPS or other navaids) was serious, even if no other errors existed.

Misalignment: mechanical mounting imprecision

Whenever this topic is discussed, certain points must be put to rest. The first concerns terminology; much of the petinent literature uses the word misalignments to describe small-angle directional uncertainty components (e.g., error in perception of downward and North, which drive errors in velocity). To avoid misinterpretation I refer to nav-axis direction uncertainty as misorientation . In the presence of rotations, mounting misalignment contributes to misorientation . Those effects, taking place promptly upon rotation of the strapdown inertial instrument assembly, stand in marked contrast to leisurely (nominal 84-minute) classical Schuler dynamics.

A third point involves error propagation and a different kind of calibration (in-flight). With the old (gimbal) mechanization, in-flight calibration could counteract much overall gyro drift effect. Glib assessments in the 1990s promoted widespread belief that the same would likewise be true for strapdown. Changing that perspective motivated the investigation and publication mentioned at the top of this blog.

The final point concerns the statistical distribution of errors. Especially with safety involved (e.g., trusting free-inertial coast error propagation), it is clearly not enough to specify RMS errors. For example, 2 arc-sec is better than 20 but what are the statistics? Furthermore there is nothing to preclude unexpected extension of duration for free-inertial coast after a missed approach followed by a large change in direction. A coauthored investigation (Farrell and vanGraas, ION-GNSS-2010 Proceedings) applies Extreme Value Theory (EVT) to outliers, showing unacceptably high incidences of large multiples (e.g., ten-sigma and beyond). To substantiate that, there’s room here for an abbreviated explanation — even in linear systems, gaussian inputs produce gaussian outputs only under very restrictive conditions.

DEAD RECKONING by GPS CARRIER PHASE

Wed, 06 Oct 2010 02:08:00 GMT

GPS Carrier Phase for Dynamics ?

The practice of dead reckoning (a figurative phrase of uncertain origin) is five centuries old. In its original form, incremental excursions were plotted on a mariner’s chart using dividers for distances, with directions obtained via compass (with corrections for magnetic variation and deviation). Those steps, based on perceived velocity over known time intervals, were accumulated until a correction became available (e.g., from a landmark or a star sighting).

Modern technology has produced more accurate means of dead reckoning, such as Doppler radar or inertial navigation systems. Addressed here is an alternative means of dead reckoning, by exploiting sequential changes in highly accurate carrier phase . The method, successfully validated in flight with GPS , easily lends itself to operation with satellites from other GNSS constellations (GALILEO, GLONASS, etc.). That interoperability is now one of the features attracting increased attention; sequential changes in carrier phase are far easier to mix than the phases themselves, and measurements formed that way are insensitive to ephemeris errors (even with satellite mislocation, changes in satellite position are precise).

Even with usage of only one constellation (i.e., GPS for the flight test results reported here), changes in carrier phase over 1-second intervals provided important benefits. Advantages to be described now will be explained in terms of limitations in the way carrier phase information is used conventionally . Phase measurements are normally expressed as a product of the L-band wavelength multiplied by a sum in the form (integer + fraction) wherein the fraction is precisely measured while the large integer must be determined. When that integer is known exactly the result is of course extremely accurate. Even the most ingenious methods of integer extraction, however, occasionally produce a highly inaccurate result. The outcome can be catastrophic and there can be an unacceptably long delay before correction is possible. Elimination of that possibility provided strong motivation for the scheme described here.

Linear phase facilitates streaming velocity with GNSS interoperability

With formation of 1-sec changes, all carrier phases can be forever ambiguous, i.e., the integers can remain unknown; they cancel in forming the sequential differences. Furthermore, discontinuities can be tolerated; a reappearing signal is instantly acceptable as soon as two successive carrier phases differ by an amount satisfying the single-measurement RAIM test. The technique is especially effective with receivers using FFT-based processing , which provides unconditional access, with no phase distortion, to all correlation cells (rather than a limited subset offered by a track loop).

Another benefit is subtle but highly significant: acceptability of sub-mask carrier phase changes. Ionospheric and tropospheric timing offsets change very little over a second. Conventional systems are designed to reject measurements from low elevation satellites. Especially in view of improved geometric spread, retention here prevents unnecessary loss of important information. Demonstration of that occurred in flight when a satelllite dropped to horizon; submask pseudoranges of course had to be rejected, but all of the 1-sec carrier phase changes were perfectly acceptable until the satellite was no longer detectable.

One additional (deeper) topic, requiring much more rigorous analysis, arises from sequential correlations among 1-sec phase change observables. The issue is thoroughly addressed and put to rest in the later sections of the 5th chapter of the book cited in the next paragraph.

Dead reckoning capability without-IMU was verified in flight, producing decimeter/sec RMS velocity errors outside of turn transients (Section 8.1.2, pages 154-162 of the book just cited). With a low-cost IMU, accuracy is illustrated in the table near the bottom of a 1-page description on this site (also appearing on page 104 of that book). All 1-sec phase increment residual magnitudes were zero or 1 cm for the seven satellites (six across-SV differences) observed at the time shown. Over almost an hour of flight at altitude (i.e., excluding takeoff, when heading uncertainty caused larger lever-arm vector errors), cm/sec RMS velocity accuracy was obtained.

SINGLE-MEASUREMENT RAIM

Sat, 02 Oct 2010 01:41:00 GMT

In January of 2005 I presented a paper “Full Integrity Test for GPS/INS” at ION NTM that later appeared in the Spring 2006 ION Journal. I’ve adapted the method to operation (1) with and (2) without IMU, obtaining RMS velocity accuracy of a centimeter/sec and a decimeter/sec, respectively, over about an hour in flight (until the flight recorder was full).

Methods I use for processing GPS data include many sharp departures from custom. Motivation for those departures arose primarily from the need for robustness. In addition to the common degradations we’ve come to expect (due to various propagation effects, planned and unplanned outages, masking or other forms of obscuration and attenuation), some looming vulnerabilities have become more threatening. Satellite aging and jamming, for example, have recently attracted increased attention. One of the means I use to achieve enhanced robustness is acceptance-testing of every GNSS observable, regardless of what other measurements may or may not be available.

Classical (Parkinson-Axelrad) RAIM testing (see, for example, my ERAIM blog ‘s background discussion) imposes requirements for supporting geometry; measurements from each satellite were validated only if more satellites with enough geometric spread enabled a sufficiently conclusive test. For many years that requirement was supported by a wealth of satellites in view, and availability was judged largely by GDOP with its various ramifications (protection limits). Even with future prospects for a multitude of GNSS satellites, however, it is now widely acknowledged that acceptable geometries cannot be guaranteed. Recent illustrations of that realization include
* use of subfilters to exploit incomplete data (Young & McGraw, ION Journal, 2003)
* Prof. Brad Parkinson’s observation at the ION-GNSS10 plenary — GNSS should have interoperability to the extent of interchangeability, enabling a fix composed of one satellite from each of four different constellations.

Among my previously noted departures from custom, two steps I’ve introduced are particularly aimed toward usage of all available measurement data. One step, dead reckoning via sequential differences in carrier phase, is addressed in another blog on this site . Described here is a summary of validation for each individual data point — whether a sequential change in carrier phase or a pseudorange — irrespective of presence or absence of any other measurement.

While matrix decompositions were used in its derivation, only simple (in fact, intuitive) computations are needed in operation . To exphasize that here, I’ll put “the cart before the horse” — readers can see the answer now and optionally omit the subsequent description of how I formed it. Here’s all you need to do: From basic Kalman filter expressions it is recalled that each scalar residual has a sensitivity vector H and a scalar variance of the form.

The ratio of each independent scalar residual to the square root of that variance is used as a normalized dimensionless test statistic. Every measurement can now be used, each with its individual variance. This almost looks too good to be true and too simple to be useful, but conformance to rigor is established on pages 121-126 and 133 of GNSS Aided Navigation and Tracking . What follows is an optional explanation, not needed for operational usage.

The key to my single-measurement RAIM approach begins with a fundamental departure from the classical matrix factorization ( QR = H ) originally proposed for parity. I’ll note here that, unless all data vector components are independent with equal variance, that original ( QR = H ) factorization will produce state estimates that won’t agree with Kalman. Immediately we have all the motivation we need for a better approach. I use the condition where U is the inverse square root of the measurement covariance matrix. At this point we exploit the definition of a priori state estimates as perceived characterizations of actual state immediately before a measurement — thus the perceived error state is by definition a null vector. That provides a set of N equations in N unknowns to combine with each individual scalar measurement, where N is 4 (for the usual three unknowns in space and one in time) or 3 (when across-satellite differences produce three unknowns in space only).

GPS Receiver Mechanization Pioneered at Ohio University

Thu, 30 Sep 2010 21:39:00 GMT

GPS codes are chosen to produce a strong response if and only if a received signal and its anticipated pattern are closely aligned in time. Conventional designs thus use correlators to ascertain that alignment. Mechanization may take various forms (e.g., comparison of early-vs-late time-shifted replicas), but dependence on the correlation is fundamental. There is also the complicating factor of additional coding superimposed for satellite ephemeris and clock information but, again, various methods have long been known for handling both forms of modulation. Tracking of the carrier phase is likewise highly developed, with capability to provide sub-wavelength accuracies.

An alternative approach using FFT computation allows replacement of all correlators and track loops. The Wiener-Khintchine theorem is well over a half-century old (actually closer to a century), but using it in this application has become feasible only recently. To implement it for GPS a receiver input’s FFT is followed with term-by-term multiplication by the FFT of each separate anticipated pattern (again with optional insertion of fractional-millisecond time shifts for further refinement and again with various means of handling the added clock-&-ephemeris modulation). According to Wiener-Khintchine, multiplication in the frequency domain corresponds to convolution in time — so the inverse FFT of the product provides the needed correlation information.

FFT processing instantly yields a number of significant benefits. The correlations are obtained for all cells, not just the limited few that would be seen by a track loop. Furthermore all cell responses are unconditionally available. Also, FFTs are not only unconditionally stable but, as an all-zero filter bank (as opposed to a loop with poles as well as zeros), the FFT provides linear phase in the passband. Expressed alternatively, no distortion in the phase-vs-frequency characteristic means constant group delay over the signal spectrum.

The FFT processing approach adapts equally well with or without IMU integration. With it, the method (called deep integration here) goes significantly beyond ultratight coupling, which was previously regarded as the ultimate achievement. Reasons for deep integration’s superiority are just the traits succinctly noted in the preceding paragraph.

Finally it is acknowledged that this fundamental discussion touches very lightly on receiver configuration, only scratching the surface. Highly recommended are the following sources plus references cited therein:

A very early analytical development by D. van Nee and A. Coenen,
“New fast GPS code-acquisition techniquee using FFT,” Electronics Letters, vol. 27, pp. 158–160, January 1991.
The early pioneering work in mechanization by Prof. Frank van Graas et. al.,
“Comparison of two approaches for GNSS receiver algorithms: batch processing and sequential processing considerations,” ION GNSS-2005
The book by Borre, Akos, Bertelsen, Rinder, and Jensen,
A software-defined GPS and Galileo receiver: A single-frequency approach (2007).

Kalman filter, strapdown, imaging, tracking, and more

Wed, 25 Aug 2010 18:17:00 GMT

An early comment sent to this site raised a question as to how long I’ve been doing this kind of work. Yes I’m an old-timer. Some of my earlier Kalman filter studies are cited in books dating back to the 1970s — e.g., Jazwinski, Stochastic Processes and Filtering Theory, 1970 (page 267); Bryson & Ho, Applied Optimal Control, 1975 (page 374); Spilker, Digital Communication by Satellite, 1977 (page 636). My first book, published by Academic Press, initially appeared in 1976. Additional manuscripts appearing prior to that book, e.g., publication #4-16 plus others, are also relevant.

Early familiarizarion with Kalman filtering and inertial navigation paid huge dividends during subsequent efforts in other areas. Those included, at first, doppler nav with a time-shared radar beam ( publication #20 ), synthetic aperture radar ( publications #21, 22, 38, 41 ), synchronization ( publication #19 ), tracking ( publications #23, 24, 28, 30, 32, 36, 39, 40, 48, 52, 54, 60, 61, 66, 67, 69 ), transfer alignment ( publications #29, 41, 44 ), software validation ( publications #34, 42 ), image fusion ( publications #43, 49 ), optimal control ( publication #33 ), plus a few others. All these efforts made it quite clear to me — there’s much more to al l this than sets of equations.

Involvement in all those fields had a side effect of delaying my entry into GPS work; I was a latecomer when the GPS pioneers were already established. GPS/GNSS is heavily involved, however, in much of my later work (latter half of my publications) — and my work in other areas produced a major benefit: The experience provided insights which, in the words of one reviewer quoted in the book description ( click here ) are either hard to find or unavailable anywhere else. Recognizing opportunities for synergism — many still absent from today’s operational systems — enabled me to cross the line into advocacy ( publications #26, 47, 55, 63, 66, 68, 73, 74, 77, 83, 84, 85, 86 ). Innovations present in the book just cited were either traceable to or enhanced by my earlier familiarization with techniques used in other areas.

EXTENDED RAIM (ERAIM) ION-GPS 1992

Sun, 04 Jul 2010 00:47:00 GMT

Almost two decades ago an idea struck me: — the way GPS measurements are validated could be changed in a straightforward way, to provide more information without affecting the navigation solutions at all.

A choice then emerged between two candidate detection methods, i.e., chi-squared and parity. The latter choice produced five equations in four unknowns, expressed with a 5×4 matrix rewritten as the product of two matrices (one orthogonal and the other upper triangular). That subdivision separated the navigation solution from a scalar containing the information needed to assess the degree of inconsistency. Systematic testing of that scalar according to probability theory was quickly developed and extended to add a sixth satellite, enabling selection of which satellite to leave out of the navigation solution. #53 – click here

The real power of this strategy comes in expansion to six satellites. A set of 6×5 matrices results, and the subdivision into orthogonal and upper triangular factors now produces six parity scalars (rather than 2×1 parity vectors – everyone understands a zero-mean random scalar). Not only are estimates obtained for measurement biases but the interpretation is crystal clear: With one biased measurement, every parity scalar has nonzero mean except the one with the faulty satellite in the suspect role. Again all navigation solutions match those produced by the original RAIM method, and fully developed probability calculations are immediately applicable. Content of the 1992 manuscript was then included with further adaptation to the common practice of using measurement differences for error cancellation, in Chapter 6 of GNSS Aided Navigation and Tracking . Additional extensions include rigorous adaptation to each individual observation independent of all others (“single-measurement RAIM”) and to multiple flawed satellites.

FUSION: MORE THAN MULTISENSOR INTEGRATION

Sat, 03 Jul 2010 17:59:00 GMT

In the early 1990s I recalled, in a manuscript (publication #49 – click here ), advocacy from years ago that probably originated from within USAF. A sharp distinction was to be drawn between “multisensor integration” for low-speed and low-volume versus “sensor fusion” for high-speed-high-volume processing. Unfortunately, separate terminology never survived; the industry uses the same vocabulary for nav update “fusion” at leisurely retes and for fusion of images (e.g., with megapixels/frame with 3-byte RGB pixels at 30 frames/sec) requiring speeds expressed in GHz.
Terminology aside, a major task for the imaging field is to recognize and categorize the degradations. Combining tracks from different sensors is a major undertaking. For obvious reasons (including but by no means limited to inertial nav error propagation and time-varying errors in imaging sensors), complexity is compounded by motion. Immediately I’ll step back and consider that from a perspective unlike concepts in common acceptance. For brevity I’ll just cite some major ingredients here:

* Inertial nav is used to provide a connection between frames taken in succession from sensors in motion. INS error propagation for these short duration cannot correctly be based on antiquated nmi/hr modeling. There are literally dozens of gyro and accelerometer error contributors, most of which are motion-sensitive and often excluded from) IMU specifications. Overbounding is thus necessary for conservative design, in effect either compromising performance or increasing data rate demand. For discussion of those error sources see relevant sections of Chapter 4 in the book whose link appears in the next item.

* It is very important not to attribute sensor stabilization errors to any tracked object's estimated state (surprisingly many operational designs violate that principle). Figure 9.3 on page 200 of my 2007 book shows a planar example for insight.

* Often there is motion of not only the sensors but also tracked objects, the masking of whose signatures -- already potentially an issue even when stationary -- will be further obscured if driven to thwart observation.

* Procedures for in-flight calibration, self-calibration, online temperature compensation, etc. are invoked. Immediately all measurement errors are then redefined to include only residual amounts due to imperfect calibration. One caveat -- any large discrete corrections should occur suddenly between -- not within -- frames (e.g., a SAR coherent integration time).

* The association problem, producing hypothetical tracks (e.g., due to crossing paths), defies perfect solution. Thus a sensor response from object `A' might be combined with subsequent response from object `B' to produce an extraneous track characterizing neither. Obviously this becomes more unwieldy with increasing density of objects responding to sensors.

* Ironically, many of the objects that complicate the association task are of little or no interest. Rocks reflect radar transmissions. Animals respond to IR sensors. Metallic objects respond to both, which raises an opportunity, to concentrate on metallic objects: accept information only from pixels with both radar and IR responses. Tracks formed after that will be far fewer and much more credible.

* Registration of image data from IR (Az/EL) and SAR (range/doppler) cells must account for big differences in pixel size, shape, and orientation. Although by no means trivial, in principle it can be done.

* Even if all algorithm development and processing implementation issues are solved, unknown terrain slopes will degrade the results. Also, undulations (as well as any structures present) in a swath will produce data gaps due to masking. How long a gap is tolerable before dropping an old track and reallocating its resources for a new one will be another design decision.

* Imaging transformation (e.g., 4x4 affine group and/or thin plate spline) applicability will depend on operational specifics.

When I was more heavily involved in this area the processing requirements for image fusion while still in raster form would have been prohibitive. Today's capabilities are far more advanced.

TONS OF INFORMATION

Tue, 29 Jun 2010 20:47:00 GMT

About fifty blogs are offered here for visitors to download and/or print. Each individual blog, with links to references which (if not under a publisher's copyright) can also be downloaded and printed from this site, summarizes a specific aspect from a chosen set of topics. A smaller number of “one-pagers” will address topics from my earlier fundamental book Integrated Aircraft Navigation . An additional few will deal with topics not covered in either of those two books. An example of the latter publicizes some useful facets of the ultra-familiar classical low-pass filter which (believe it or not – after all these years) have remained obscure. The overall span of subjects (all firmly supported by experience as well as theory) ranges from elementary to advanced, in some cases relatively new and therefore largely unknown.

Modern estimation in both block (weighted least squares) and sequential (Kalman filtering, with Battin's derivation - much easier to follow than Kalman's) form, with their interrelationship developed quite far, enabling "plant noise" levels to be prescribed in closed-form, also providing highly unusual insight into sequentially correlated measurement errors; chi-squared residuals; implications of optimality during transients; need for conservatism in modeling; sensitivity of matrix-vs-vector extrapolation ("do's and don'ts"); application-dependence of commonality and uniqueness features; quantification

of observability and effects of augmentation on it; duality among a wide scope of navigation modes; commonly overlooked duality between tracking and short-term inertial nav error propagation; when "correction-to-the-adjustment"

terms can and can't be omitted; suboptimal (equal-eigenvalues) estimation with steady-state performance indistinguishable from optimal; all fully supported by theory and experience

Basic building-blocks for attitude expressions: superiority of quaternions and direction cosines over Euler angles, due to singularity ("gimbal lock" at 90-deg for x-y-z sequence) and at 0-deg for z-x-z sequences used for orbits

GPS issues related to the top-priority goal of robustness: beyond elementary (4-state and 8-state) formulations; duality of pseudorange and phase ambiguity; exploitation of modern processing capabilities in GPS/GNSS receivers; carrier phase as integrated doppler vs frequency data; 1-sec sequential phase changes (MUCH easier to mix across constellations, negligible sequential changes in IONO/TROPO propagation, ambiguity resolution not needed, instant reacquisition, no-mask angle needed); streaming velocity for dead reckoning with segmentation of position fixes; differential operation -- differencing across satellites, receivers, and time; handling correlations from differencing; orthogonalization for simple QR factorization; measurement relocation in time and lever-arm adjustment; E(Extended)RAIM; D(Differential)RAIM; necessity of weighting in single-measurement RAIM with pseudoranges and carrier phases, concurrently; sample flight test results showing state-of-the-art accuracies in dynamics (e.g., cm/sec RMS velocity error and tenths-mrad leveling) with a low-cost IMU; revisit of the same flight segment, achieving decimeter/sec RMS velocity error without any IMU

Tracking (with subdivision into more than fifteen topics including a littoral environment operation with hundreds of ships present; orbit determination; usage of Lambert's law; surface-to-air (subdivided into ground-to-air and tracking from ships), surface-to-surface (again with the same subdivision), air-to-surface, air-to-air; reentry vehicles; usage of stable coordinate frames; linearity in both dynamics and measurements; Mode-S squitters for mutual surveillance and collision avoidance in crowded airspace; multiple track output usage (placement of gates, antenna steering, file maintenance); crucial importance of transmitting measurements rather than coordinates; extension to noncooperative objects, critical distinction (elsewhere blurred) between errors in tracking and stabilization; sucessfully accomplished concurrent track of

multiple objects with electronically steered beams; bistatic and multistatic operation; postprocessing to form familiar parameters from estimator outputs; short-range projectiles over "flat-earth" - plus many more)

Processing of inertial data - incrementing of position, velocity, attitude; straightforward state-of-the-art algorithms for complete metamorphosis from raw gyro and accelerometer samples into final 3-D position, velocity, and attitude; motion-sensitive inertial instrument errors; coning; sculling; critical distinction between misalignment (imperfect mechanical mounting) vs misorientation; adaptive accommodation of gyro scale factor and misalignment errors; instability of unaided vertical channel; azimuth pseudomeasurement; near-universal misconceptions connected to free-inertial coast

Support functions (transfer alignment; SAR motion compensation; stabilization of images; sensor control mechanizations; synchronization; determination of track retention probability)

Vision-for-the-future with maximum situation awareness for all cooperating participants in a scenario; Role of Interface (implications of singularities, RAIM, Differential GPS, etc.), software modularity, reuse, coordination).

KALMAN FILTER or SUBOPTIMAL – DOES IT MATTER?

Tue, 29 Jun 2010 18:56:00 GMT

For steady-state a suboptimal estimator can be designed with near-optimal performance. A Kalman filter, though, optimizes accuracy during transients too – provided that the model is known and linear. Immediately we’ll invoke the “almost/most/if” qualification: an extended Kalman filter (EKF) is almost optimum, throughout most of its operation, if the model is almost linear and modeling errors are held in check via process noise. Rather than presenting justification here I’ll cite a set of “do’s-and-dont’s” – validated by long experience – from Section 2.9 of GNSS Aided Navigation and Tracking , with GPS/INS flight test data included. Eqs. (9.9)-(9.19) of that same reference provides simple design equations for alpha-beta and alpha-beta-gamma trackers that have consistently produced success in operation.

First we’ll note that suboptimal is not equated to “constant gain” – if for no other reason, the time between measurements will vary in many systems. That’s quite easily accommodated by the alpha-beta[-gamma] designs just mentioned. There are additional reasons, though, that can be illustrated by addressing a taxing situation for initiating a radar track file in close range air-to-air encounters between two fighter jets. The target’s (i.e., tracked object’s) cross-range velocity at lock-on time is unknown. It could be 800 ft/sec, for example, in which case the tracker’s initial velocity error has at least that 800-ft/sec component. With any additional unknown component of along-range velocity the target may have at that instant (doppler, if observed, might not yet be trusted to represent range rate dynamics), the tracker’s initial velocity error will then exceed 800 ft/sec. The transient at acquisition could easily be further complicated by acceleration. Anyone familiar with servo pull-in dynamics will immediately see how the transient can reach significantly beyond the initial error – very fast – in multiple directions (e.g., East/West and North/South). Since we’re not at all comfortable with velocity errors on the order of 1000 ft/sec, the task is to wash that out ASAP.

A Kalman filter having accurate knowledge of the initial [P] matrix would breeze through this challenge. An excellent example of its role is provided by this transient behavior. Knowledge of that matrix is tantamount to knowing whether – at initiation time – the tracker’s North velocity error is positively or negatively correlated (i.e., likely to have the same or opposite sign) as its North position error, likewise for East velocity error with same-vs-opposite sign of North acceleration error, and likewise … all combinations – not only the signs but also the RMS amounts. Of course that’s completely unrealistic. So now what?

Suboptimal gain sets phased in at the right times can handle this. For a simple illustration, let a 3-dimensional tracker, divided into three separable 3-state (position/speed/acceleration) single-direction channels, have a 20-Hz update rate. If the first few updates have gains of 0.5 or more for position only , even a huge position error can be quickly brought down near sensor-error levels before accompanying errors in dynamics have much time to propagate. Then after that many (“K1”) position corrections, a position-&-speed update phase can be initiated, using the alpha-beta tracker gains related as shown in Eq. (9.12) of the reference cited above. Duration of that phase is devised to last only as long as necessary to reduce speed error to design levels (which will be proportional to measurement error divided by that duration). After the total number of corrections has reached that intended design value (“K2”), the alpha-beta-gamma phase can start with gains related according to Eqs. (9.18-19) of that same reference. That phase continues until the total corrections count reaches “K3” at which time acceleration error is reduced to an amount inversely proportional to the square of (K3-K2). Gains thereafter may conform to Kalman filter weighting.

This example is not intended to advocate substituting suboptimal for optimal designs just anywhere. Separation of 3-dimensional trackers into 3-state single-direction channels is often permissible (and sometimes even highly advisable), but – as shown in the cited reference – sometimes inappropriate. Where it is permitted, use it; solving the unknown-P-zero problem is especially important in applications of this type. A word to the wise: Do not ( repeat : do not ) make the update counts K1,K2,etc. programmable. If you do, someone unfamiliar with the reasoning above will experiment, allowing resets to values producing very prolonged back-and-forth transfer of errors among position and dynamics (one gets worse as another improves; then vice-versa). When that spectacle is seen by nontechnical administrators, your image in their minds will forever be indelibly painted with that long drawn-out transient veering back and forth between plus and minus extreme levels.

Another slice-of-advice: Even if inputs are extremely erratic, your tracker must maintain high responsiveness (for sensor sightline stabilization at short range and for range[/doppler] gate placement at any range) – but – the outside world doesn’t have to witness the results of that “hitchy-hatchy” from wildly erratic inputs. So: don’t change the tracker but what goes outside can be low-pass filtered to ease interpretation of the display . Since that “hides the system’s warts” without attacking the problem at its roots, the resulting lag (possibly with accompanying distortion) can draw criticism.

COLLISION AVOIDANCE BY DECELERATION

Tue, 29 Jun 2010 02:13:00 GMT

As an alternative to TCAS in air and ASDE on ground, all facets of collision avoidance ( see 9-minute video ) can be supplanted with vast improvement:

My previous investigations ( publication #61 and #66 , combined with publication #85 as well as Chapter 9 of GNSS Aided Navigation and Tracking ) provided in-depth analyses. The control aspect of the problem is addressed here. This introductory discussion involves only two participants, initially on a coaltitude collision course. One (the “intruder”) continues with his path unchanged (so that the method could remain applicable for encounters between a participant and a non-participant tracked by radar or optical sensors). The other (“evader”) decelerates to change projected miss distance to a chosen design value. This simplest-of-all scenarios can readily be extended to encounters at different altitudes and, by reapplying the method to all users wherever projected miss distance falls below a designated threshold, to multiple-participant cases.

Considered here are simple scenarios with aircraft initially on a collision course at angles from 30 to 130 degrees between their velocity vectors. Those limits can of course be changed but, the closer the paths are to collinear the more deceleration is required to prevent a collision (in the limit – direct head-on – no amount of deceleration can suffice; turns are required instead). Turns can be addressed in the future; here we briefly discuss the 30-to-130 degree span.

In Coordinates Magazine and again as applied to UAVs it was shown that, over a wide combination of intruder speed, evader speed, and angles (within the 30-to-130 degree span just noted), the required amount of evader speed reduction is modest. A linearized approximation can be derived intuitively from scenario parameter values. The speeds and the angle determine a closing range rate, while closest approach time is near the initial time-to-go (ratio of initial distance to closing rate) though deceleration produces a difference. The projection of evader speed reduction along the relative velocity vector direction has approximately that much time to build up 500 to 1000 meters of accumulated horizontal separation. Initiation of the speed change that far in advance allows the dynamics to be gradual, in marked contrast to the sudden TCAS maneuver. To avoid a wake problem, the evader’s aim point can be directed to a few hundred feet above the original coaltitude. Continuous tracking of the intruder allows the evader to perform repetitive trim adjustments.

A program with results illustrating this scheme will not fit on a one-page summary, but it comes as no surprise that, with accurate tracks established well in advance (a minute or two prior to closest approach time), a modest deceleration can successfully avert collisions.

TRACKING: CARTESIAN vs SPHERICAL COORDINATES

Sat, 12 Jun 2010 18:38:00 GMT

A widespread missed opportunity began many years ago and continues to this day. It is still widely believed that significant nonlinearity is inescapable in a tracker – whether for dynamics with spherical coordinates or for measurements with Cartesian coordinates. The first half of that is definitely true for dynamics using the classical (range/elevation/azimuth) frame in air-to-air encounters at close range; we’ll take that issue first here.

One question that could be raised immediately might sound something line this: Since expressing dynamics in a range/elevation/azimuth frame causes so many problems (not only linearity but many more, to be discussed shortly), why even consider that as a candidate approach? Old-timers will readily recall that analog radars provided no other choice. They had range trackers, while angle tracking was done separately in outer loops with bandwidths narrow in comparison to inner stabilization loops maintained via antenna-mounted gyros. Couldn’t that still be done after digitization? Yes – in fact, it was done. In the early 1970s I reviewed a paper for IEEE showing just that. I gave it the green light because it was correct. For my own design, though, I used a Cartesian frame ( publication #24, 26, 28, 30, 32, 36, 60, 61, 66, and 69 -- It is worth noting that #66 combines #60 and #61 ). No contest.

The widely recognized nonlinear degradation of a range/elevation/azimuth representation for dynamics only begins to explain why that choice is fraught with problems. For one issue, that loop-within-a-loop situation imposed a demand on inner stabilization bandwidth; if too low it would compromise the overall operation’s stability. Alternatively that requirement could be viewed as a constraint on track loop responsiveness. Another very serious issue was the interfacing requirements; gyro and accelerometer data had to be used in that track configuration (which added another burden of time-tagging plus another degradation from time-tag imperfections). Still another limitation was inability to represent multiple track files; they aren’t all in the same direction and their Line-of-Sight rates are anything but uniform. Finally, if handoff of a track file became necessary (e.g., from a forward-looking to a side-looking sensor during fly-by), I wouldn’t want to inherit that task with (range/elevation/azimuth) dynamics at close but wildly changing distances and geometries.

The item just noted brings up a favorite example raised by my coauthor of publication #24 and 32 : Two aircraft approach each other on parallel tracks separated by 1000 ft. With each having constant 1000 ft/sec groundspeed, the centripetal acceleration ( see Ex. 8-12c on page 295 of Integrated Aircraft Navigation ) at the instant of closest approach (sidelong position) is

or about 125 g. The example is extreme but, even with more moderate encounters no range track loop can perform adequately in both responsiveness and noise rejection. The second derivative of scalar distance is very high in close range scenarios.

Now a comparison to the Cartesian frame can begin. Instantly the “problem” just shown disappears. There isn’t any acceleration at all; all Cartesian velocity components are constant. Then handoff is easy too. We’re off to an excellent start. Next: interfacing – that’s also easy – never mind the gyros and accelerometers, just adopt the INS nav frame as the Cartesian reference for tracking and use the nav computer output. Eq. (2.13) of GNSS Aided Navigation and Tracking shows that it’s just as easy to track from a maneuvering fighter jet as it is while at rest. Stabilization loop? It isn’t inside any other loop; let it have whatever bandwidth it has. Separate the stabilization offsets from tracker inputs as illustrated in Figure (9.2) of GNSS Aided Navigation and Tracking . That same “dot-off-the-crosshairs” figure, with its accompanying analysis (Section 9.2.2), readily reduces to negligible levels any measurement nonlinearities as well. Multiple targets? Again, easy – just maintain one track file for each object being tracked.

That was fast, wasn’t it?

Low pass filter

Fri, 11 Jun 2010 17:58:00 GMT

Decisions are made, understandably, on the basis of a decision-maker’s beliefs. In general, the better the knowledge base, the better the anticipated outcome. Inevitably there are times when choices must be made from incomplete information. Even that can still produce success, but the likelihood of a favorable outcome depends on recognition of those uncertainties. Likelihood of an un favorable outcome, then, increases when those information gaps go unrecognized. That is, when we are unaware of the fact that we don’t know (“don’t-know-squared”). To make that case for this site I’ll use an example from an area outside of navigation and tracking:

One field that has received thorough investigation is the study of a low-pass filter. Users of those commonly believe that they know all that is needed to make the wisest design selection. Quite often they know much – but not everything that would be useful to them. It is not unusual for a maximally-flat (Butterworth) attenuation characteristic to be chosen while assuming that nothing much can be done about the accompanying nonlinear phase; latency often precludes usage of phase equalizers. It is known – but not widely known – that a trade-off has been available for decades. A near -linear phase characteristic over the passband can be realized if some of the attenuation requirements can be relaxed. Full details can be found in:

Handbook of Filter Synthesis by Anatol I. Zverev
ISBN 10: 0471986801 / 0-471-98680-1 ISBN 13: 9780471986805
Filtering in the Time and Frequency Domains by Herman J. Blinchikoff and Anatol I. Zverev ISBN-10: 1884932177 ISBN-13: 978-1884932175

Already I’ve said as much as I intend to say here about low-pass filters. To go this far without misinterpreting some points I found it necessary to consult a coauthor (Blinchikoff) of the second reference just cited. The rest of the blogs on this site involve navigation and tracking – where avoidance of don’t-know-squared is still very much an issue. Examples from those areas won’t all be obvious (e.g., a pilot believing his broken altimeter), but there is much to be gained from “looking under the hood” and uncovering missed opportunities. If we’re willing to pursue that, let me assure you that vast improvements in performance are available.

The Pace of Change in the Industry

Sat, 29 May 2010 19:39:00 GMT

As a lifelong techie I’m constantly reminded of erratic pacing for changes in our industry. Hardware and software lurch at dizzying rates while advanced concepts, with dramatic potential for exploiting improved technology, languish unused for years. Whether in GPS/GNSS receiver configurations, surveillance, collision avoidance, or various other areas, needed solutions await industry’s willingness to change the status quo. A basic function in today’s systems is source-to-destination data transmission. Quite often an urgent need can be met, not by more precision nor higher data rates nor larger capacities, but simply a different selection of information content.

Space limitations preclude full elaboration here; see other parts of this site and the references cited therein. Although today’s modus operandi limits both military and commercial systems. I’m not implying that inertia plus oversimplification in methodologies are entirely to blame for “missing the boat” in all instances. Additional factors are well known (e.g., safety often requires smooth – thus, coordinated – “old-to-new” transitions). It is striking, though, to witness how much effect the one facet noted above (selection of information content) can exert on overall performance. I elaborate on that in several publications – many available on this site.

No criticism is intended nor implied here; yesteryear’s designs lacked access to today’s technology, and other lifelong techies have a different set of uncommon insights (not unusual). To fortify claims just made, I’ll do two quick things. First, for just one of many topics with potential (but unused) enormous improvement I show at this site – a recognized real-world example: collision avoidance, in both two (runway incursions) and three (near miss in-air) dimensions. Second, in addition to the 100+ book pages viewable from this site, I cite a small but representative fraction chosen from about 90 manuscripts I wrote or coauthored:

In applications across-the-board (in-air, maritime, space-related, or on land), depth of insight despite complexity is a make-or-break factor. Although that merely states the obvious, we repeatedly observe adherence to older techniques that could not capitalize on capabilities offered by recent technological advances. In addition to the previously mentioned “slower-is-safer” caution it is instructive to recall some further restraints. These challenges must be met to avoid failure, as described among references cited herein (“The industry can either adopt changes or continue to settle for performance levels at a minor fraction of the intrinsic capabilities available from our present and future systems.)” Claims I make here can invite skepticism -- fair enough -- but those willing to explore in depth these references will see potential for unprecedented benefits.