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 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.

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 breathtaking. 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.

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
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The number of runway incursions, as shown on an FAA URL  was nearly a thousand in FY 2011 and 1150 for FY 2012.  A subsequent article shows renewed interest in their prevention.

A hundredfold 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 an accompanying blog.  A publication describing highly favorable results in air (3-D) could readily extend to 2-D (surface).

A 1996 crash that killed U.S. Commerce Secretary Ron Brown drew attention to a problem that has caused thousands of airline fatalities.  Controlled flight into terrain (CFIT) results from an autopilot driven by erroneous information regarding aircraft‘s flight path relative to its surroundings.  This writer narrowly escaped death in early January 1981 when an errant foreign airliner very nearly collided with the World Trade Center (that time it would have been accidental); an alert air traffic controller issued a turn directive just in time.  A highly informative IEEE-AES Systems Journal article by Swihart et.al. —
…. “Automatic Ground Collision Avoidance System Design, Integration, and Test” (May 2011, pp.-4-11)
addresses CFIT while envisioning, near the end, future extension to unmanned aircraft.  The authors correctly describe the effort as the beginning of a long-awaited development with a huge payoff in lives to be saved and, secondarily, in vehicles not destroyed.  As proof of my full concurrence — both with the intent and with the “long-awaited” characterization — I cite the following:

* a “GPS for Collision Avoidance” seminar I prepared in 2000 (hardly anyone attended — no funding, no interest — but safety shouldn’t take a back seat to economics).
* two coauthored papers (ICNS 2009 and ION-GNSS-2011) resulting from recent low-level support to Ohio Univ. by NASA.


It remains true to this day: much more needs to be done.  Without significant increase in development, life will be increasingly hazardous.  Both heavier traffic and unmanned aircraft will contribute to the increased danger.

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:

  • INTEGRATION – one system for both 2-D (runway incursions) and 3-D (in-air)
  • AUTONOMY – no ground station corrections required
  • COMMUNICATION – interrogation/response replaced by ModeS squitter operation
  • COORDINATION – coordinated squitter scheduling eliminates garble
  • TRACKING – all tracks maintained with GPS pseudoranges in data packets
  • DYNAMICS – tracks provide optimally estimated velocity as well as position
  • TIMELINESS – history of dynamics with position counteracts latency
  • MULTITARGET HANDLING – every participant can track every other participant
  • CONTROL – collisions avoided by deceleration rather than climb/dive

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 for all but the last of these items.  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.

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 below. 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 – some 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’ll 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:

  1. “System Integration: Performance Doesn’t Measure Up,” NAECON Symposium, Dayton Ohio, 1993 —       later printed in IEEE-AES Systems Journal
  2. “Send Measurements, not Coordinates (Co-au)” IONJ, Fall 1999, pp. 203-215
  3. Unfinished Business–Glaring Absences from the Achievement List IEEE PLANS, Monterey CA 2004
  4. “ADSB (2nd-) Best Foot Forward?” (Co-au), Air Traffic Control Journal, v50  Summer 2008, pp 17-18.
  5. InsideGNSS Fall 2008, pp.29-32
  6. GPSWorld Dec 2009, pp. 8, 10, 12
  7. Robust Design for  GNSS Integration ION-GNSS, Savannah GA, Sept. 2008
  8. Aging SV’s – We Have Solutions ION-GNSS, Savannah GA, Sept. 2009

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” constraint it is instructive to consider some further restraints:

  • Up-front needs face resistance from creatures of habit with short-term focus.
  • Younger workers, brilliantly adept with computers (operating systems, data flow, etc.) are less familiar with the functional intent of the design.
  • Many system designers have the “shoe on the other foot” (versed in theory but lacking depth of software coding or computer operations in general).
  • Emphasis on management technique produces decision-makers with insufficient technical preparedness.

These challenges must be met to avoid failure, as described in the sixth reference cited above which ends by stating “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 much skepticism. Fair enough, but those willing to explore in depth the references just cited will see potential for unprecedented benefits.