Once again I am privileged to work with Ohio University Prof. Frank vanGraas, in presenting tutorial sessions at the Institute of Navigation’s GNSS-17 conference. For 2017, as in several consecutive previous years, two sessions will cover integrated navigation with Kalman filtering.  Descriptions of the part 1 session and part 2 session are now available online.

By way of background: The first session is introductory.  Each attendee will be 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-members online tutorial is recommended.  Also my three-part matrix tutorial video will be 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 is given to those attending the second session. attending the second session.



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. 

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 three directions translates into a billion times less volume of uncertainty — or, in just two dimensions at fixed altitude, a million times less area. 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 within the past few years 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?”

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 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 references for satellite navigation, widely acclaimed and far more thorough than any attempted paraphrasing could have provided.
* a pre-GPS book Integrated Aircraft Navigation covering fundamentals of
Kalman filtering and inertial navigation.

Secretary of Defense Ashton Carter’s recent statement “I hate GPS” naturally creates much concern within the navigation community. The July-August issue of InsideGNSS 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.


An overdue update of this site was recently done. The “Video” panel has recent additions, and a ‘miscellaneous’ (“Misc”) panel was added (to describe some work that was never published and/or never completed).  From time to time more uploads will be added to that and other panels (e.g., “Published Articles” or “1 Page Summaries” plus blogs. URLs that were changed after being cited here are being either replaced or deleted.

Several external URLs (e.g., at zine sites that hosted columns I wrote) were subsequently changed, causing broken links.  I had to fix those from time to time (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.

One final observation: It is not “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 is more important to me.

In regard to integration of satnav with IMU — my column in the current issue of GPSWorld has a critique of common practice for loose coupling — http://gpsworld.com/expert-advice-loose-coupling-and-whats-wrong-with-it/        In brief, if pseudo measurements must be accommodated (e.g., because of interface limitations), I strongly recommend using position only — not position and velocity. Velocity information is already implicit in position history; using both from a receiver’s 8 state EKF violates independence and obstructs aiding. Aiding the dynamics is the IMU’s job; allowing derived 8-state pseudovelocity to overrule it misrepresents current velocity as if it were equal to an average over some past period. That won’t be true when the velocity vector changes with time. Block diagrams showing 8-state pseudo velocity updating are seemingly everywhere — but real world behavior doesn’t depend on how we characterize it.

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 website JamesLFarrell.com). It can be helpful also to point out other descriptions e.g., 1-sec carrier phase usage

60MinutesVideoPicOn 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, that collapse of a particular bridge was imminent. Those responsible, to escape subsequent condemnation, would promptly find funds for the essential repairs.  The 60 Minutes program showed an instance of exactly that, arising from evidence discovered purely by chance.
QuakeVideoEndPicOK, maybe that’s obvious, but how could evidence come by design?  A year and a half ago I offered a way to approach that,  supported by a successful experience analyzing precise daily recordings from monitoring stations surrounding Tohoku (March 2011); both in a Detailed Video Presentation  and a short summary are available.  For application to infrastructure the details would differ, but certain key features would remain pertinent.  Collapse of a steel bridge would be preceded by change in shape of one or more structural members.  
The same is true for one made of concrete mixed with polyvinyl alcohol fibers (e.g., used in Japan and New Zealand). Permanent deformation occurs when the elastic limit is exceeded. Gradual accumulation of deformed members would provide early warning. Just as 3-dimensional shape state analysis identified the station nearest a quake epicenter, location of critical structural members would be revealed by a program using sequences of infrastructure measurements.


To access the free offer below, become a subscriber by clicking here now. The free video viewing will be available to all subscribers beginning on the afternoon of November 15th 

I’m giving free access to a 20-minute video, available for three days to all subscribers. It is the first of three segments I’ve put together for two reasons:
1) Dearth of time during a short course doesn’t allow adequate coverage of applicable matrix theory in class.
2) The material was organized to drive home a fundamental point: Math without insight is grossly inadequate. That lesson will be useful to professors, instructors, and mentors as well as designers.
I start with a no-math real-world example dramatically illustrating preference for insight over blind acceptance of computer outputs.
Each of the three parts has a preview that can be watched free at any time. Click Here
If you click on any section, options include a preview for no cost (white circle on the right). Attendees of any course I teach will receive free 3-day access all three parts, and others (e.g., students or trainees) would also benefit from this information. An admission: The recording was done during hay-fever season; I sound (and look) like it. That’s unimportant in comparison to the message.
HomePageNewBookPicIn addition you will receive a 100 page excerpt form my latest book GNSS Aided Navigation and Tracking
My website now has excerpts from a wide variety of topics, all of which can be expanded further into helpful learning aids — backed by a long history of real-world experience and insights very much in need today. Occasionally I make incremental additions generated for release. As always, subscribers have the option for subsequent opt-out with no danger of further contact, spam, etc.