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. 

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 . I also prepared a video with a preview that can be seen free of charge (just click inside the white circle). Finally, there’s also a blog

The one remaining item needing explanation will be covered here where the last video is entitled 3D Deformation Extraction for Morphometrics. Those who follow that video 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.

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.


After wide distribution of my recent InsideGNSS 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
will 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 trackinga 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 averaging
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

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.

Vulnerability of everyday life in America, through vulnerability of GPS, is not widely recognized. That gap in awareness would be filled instantly if GPS ceased to operate. Functions we take for granted, not only for transportation but also communication, affect multiple processes in ways vitally dependent on satellite navigation. Its steady improvement over recent decades has spawned increasing usage of its capabilities — and growing reliance on continuation of its spectacular success.
Far-reaching ramifications of that theme were analyzed in depth at a June 11 gathering of the National Space-Based Positioning, Navigation, and Timing Advisory Board. After kickoff by the Space Agency Headquarters Executive Director, followed by an opening presentation from the father-of-GPS, several speakers addressed a broad range of topics. Many of those involved the crucial importance of protecting and augmenting GPS, plus specific present and future steps planned to accomplish that.
Much of the discussion covered items under military or government control, i.e., the satellites or ground stations used to track and communicate with them. A minority aimed at protective measures devised for user equipment — receivers on ships, airborne, or on the ground. Toward the end of the day my own presentation expressed recommendations, some obvious and some more subtle, demonstrably capable of producing dramatic improvements in both accuracy and robustness. While those considerations revisited advocacy I’ve offered in the past, I was able to say-it-with-data. Immediately following my title slide, in-flight results showed precise velocity — in both navigation and tracking — by using the methods proposed.
An example will illustrate the effectiveness of those methods: the tracking demonstration obtained velocity accuracy a thousand times better than official ratings quoted for the latest-and-greatest Next Generation Air Transportation System — Automatic Dependent Surveillance Broadcast (ADSB). Although that test was just a first step (no all-encompassing claims are being attempted), the huge advantage in velocity — which directly affects collision avoidance capability — clearly warrants further investigation. There’s much more (my last page listed several URLs); sufficient for this summary is a reminder that monumental improvements are achievable, just through simple adjustments to receiver interfaces. A few suppliers already make measurement data available; another post will cover relevant opportunities within the industry.


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.