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 —        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 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.


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 several 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.

A video completed recently provides just enough matrix theory needed for Kalman filtering. It’s available for  (1) purchase or 72-hour rent at low cost or (2) free to those attending courses I teach in 2014 or after (because the short durations don’t allow time to cover it). The one-hour presentation is divided into three sections. Each section has a preview, freely viewable.



The first section, with almost NO 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 (e.g., doubled or possibly more) for easy visualization, it becomes clear why insight is every bit as important as the math.


EmailMarketingPicFor some viewers the importance of insight alone will be of sufficient interest with no need for the latter two sections. Others, particularly novices aspiring to be designers, will find the math presentation extremely helpful. Straight to the point for each step where matrices are applied, it is just the type of information I was earnestly seeking years ago, whole “pulling teeth” to extract clarification of ONLY NECESSARY theory without OVER simplification.


The presentation supplies matrix theory 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 saw as teenagers in college.


Useful for either introduction or review, there is no better way to summarize this material than to repeat one word that matters beyond all else — INSIGHT.

Surveillance with GPS/GNSS



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; hundredsof 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 pseudomeasurement 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.