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?”
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.
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.
A LinkedIn discussion centered on the Future Airborne Capability Environment (FACE) standard contained an important observation concerning certification. Granted — requirements for validation, with acceptance by governing agencies, definitely are essential for safety. What follows here is advocacy for a proposed way to realize the common avionics benefits offered by FACE while retaining (and in fact, improving) the process of certification. Reasoning is based on three major items:
* CHANGE. In many respects this has necessitated improved standards.
* HISTORY. Spectacular failures in what we have now are widely documented.
* COST. The status quo is (and, for a long time, has been) unaffordable.
In regard to the first item: the pace of change in so many areas (hardware, software, operating systems, data communication, etc., etc., etc.) — and the effects on procurement cycles — are well known. How can certification remain unchanged when nothing else does? That argument would be undercut if the process had a rock solid track record — but that theme would not be supported by the second item — history:
Myriad shortcomings of existing operational systems are so pervasive that no one is considered a “loose cannon” for openly discussing them. Any of my horror stories — too strange and too numerous to be revisited here — would be trumped anyway by a document from the government itself. GAO-08-467SP, in 2008, described outlandish cost overruns, schedule delays, and deficient technical performance in the defense industry. That 3-way combination speaks for itself. Now a significant addition: the certification process has not been at all immune to serious flaws. The first-ever certified GPS receiver is now well known to have failed spectacularly in multiple facets of integrity testing by another manufacturer. It is readily acknowledged that correction of those early problems is quite credible, but one issue is inescapable: Historical proof of flightworthiness improperly bestowed — with proprietary rights accepted for algorithms and tests –- happened, and that was not widely known until much later.
There is still more, including integrity failure probability limits missed by orders-of-magnitude in certified GPS receivers, severe limitations of GO/NO-GO testing, and failed attempts to gain approval to set requirements for correcting those plus other deficiencies. For brevity here, those issues are covered by citing the fifth page from another related reference.
The final item is, after years of fruitless talk about cost reduction, being acknowledged — we can’t do what we’ve been doing any more. With dollars being the ultimate driver of so many decisions, we might finally see the necessary break from ingrained habits. FACE already addresses the issues and the requisite justifications. To make it all happen, two essential ingredients are
* raw-data-across-the-board, and
* nonproprietary software, with standardization under government control.
Flight-validated algorithms already in existence can be converted (e.g., from proof-of-concept to in-flight real-time form) according to government specification, by small groups more interested in engineering than in dollars (yes, that does exist). The payoff in cost savings can be huge.
Significant momentum is evolving toward a role for Open System Architecture (OSA) applied to radar. My observations in connection with that, voiced in a short LinkedIn discussion, seem worth repeating here.
One step could add major impact to this development: Rather than position (or relative position) outputs, provide measured range, azimuth, elevation (doppler could optionally be added if applicable) on the output interface. That simple step would vastly improve effectiveness of track file maintenance. Before attempting to describe all reasons for improved performance, two obvious benefits can be identified first:
* ability to use partial information (e.g., range-only or, for passive operation, angle-only)
* proper weighting of data for updating track state estimates.
The first item is self-evident. The second arises from common-sense attachment of greater value to the most accurate information. An explanation:
One-sigma error ellipsoids for individual radar fixes are not spherical (not a beachball shape but more like a flattened beachball), even at close range. At longer distances the shape progresses from a frisbee to a pancake to a DVD. Kalman filtering has enabled us to capitalize on that feature for over a half-century. Without exploiting it, we effectively treat separate radar-derived “coordinates” by intersecting volumes in space that are common to overlapping spheres. Resulting uncertainty volume is enormously larger than it should be.
The feature just noted shows up dramatically when mixing data among multiple platforms. Consider cooperative engagement whereby participants, all tracking each other via network-transmitted GPS observations, share radar observations from an unknown non-participant. Share measurements or coordinates? No contest; multiple lines crossing from different directions can offer best (i.e., along-range) accuracies applicable in 3-D.
That fact (i.e., combining data from different sensors and different platforms further dramatizes available improvements) doesn’t diminish the basic issue; even with a time history of data from only one radar, a designer with direct measurements available — instead of, not in addition to, coordinates — can provide incomparably superior performance.
“Send Measurements not Coordinates” (1999; #66 from the “Published Articles” panel, opening with eight rock-solid reasons) was aimed at GPS rather than radar. Many of the principles are the same when mixing data with information from other platforms — and from other sensors such as GPS. There is no reason, in fact, why data from satellite navigation and radar can’t be combined in the same estimation algorithm. That practice hasn’t evolved but the historical separation of operations (e.g., navigation and surveillance), arising from old equipment limitations, should no longer be a constraint. Moreover, with focus shifted from tracking to navigation, integration with additional (e.g., inertial) data offers still more reasons for using direct measurements. Rather than loose integration, superior benefits are widely known to result as the sophistication progresses forward (tight. ultratight, and deep integration).
Further elaborations on “casting off our old habits” appear from different perspectives in various blogs, one-pagers, and a few manuscripts available at this site. If your library has a copy of GNSS Aided Navigation & Tracking pages 203-4 show a way to implement the cooperative sharing of radar data obtained from a non-participant, among participants tracking each other via the mutual surveillance and tracking approach defined earlier in that same chapter.
Because so many operational systems (in fact, a vast majority) use reports in the form of coordinates, reiteration is warranted. The central issue is the content, not the amount, of data. Rather than coordinates, provide accurately time-stamped direct measurements with links connected to whichever platform observed the data (e.g., for satnav — pseudoranges; for radar — range, azimuth, elevation). Those links are automatically attached when Mode-S extended squiter (e.g., chosen for ADSB) is the means for conveying the data. For message content, strictly disallow “massaging the data beyond the light of day” (e.g., by unknown processes, with uncertain timing, … ) which invariably results in enormous loss of performance in common occurrence today.
Before GPS took over so many operations by storm (e.g., navigation,tracking, timing, surveying, etc.), designers had access to other — far less capable — provisions. That condition forced our hands; to derive maximum benefit from what was available, we had to extract full information content from those provisions. Now that GPS is subjected to challenges (aging, jamming, spoofing, etc.), some of those older methods are receiving increased scrutiny. Recently I’ve received renewed interest in areas I analyzed decades ago. Old publications from two of those areas are discussed here: 1) attitude determination and 2) nav integration.
“Attitude Determination by Kalman Filtering” is the title of three documents I had published. In reverse sequence they are:
1) Automatica (IFAC Journal), v6 1970, pp. 419-430,
2) my Ph.D. dissertation (Univ. of Maryland, 1967),
3) NASA CR-598, Sept., 1966.
As indicated by the last reference, the work was the result of a contractual study sponsored by NASA (specifically Goddard Space Flight Center – GSFC – in Greenbelt Maryland). I was working for Wetinghouse Defense and Space Center at the time. The proposal I had written to win this contract cited my work prior to then, in both modern estimation (“Simulation of a Minimum Variance OrbitalNavigation System,” AIAA JSR v 3 Jan 1966 pp. 91-98) and attitude computation (“Performance of Strapdown Inertial Attitude Reference Systems,” AIAA JSR v 3 Sept 1966, pp. 1340-1347). Let me hasten to explain the dates of those Journal publications: each followed its inclusion at an AIAA-sponsored conference, about a year earlier.
By the mid-1960s there was an appreciable amount of validation for Kalmen filtering applied to determination of orbits (that track record was convincing) but not yet for attitude. A GSFC-sponsored investigation was then planned — the very first one for attitude using modern estimation methods. GSFC management understandably wanted that contractual investigation to be performed by someone with demonstrable experience in both Kalman filtering and rotational dynamics. In those days that combination was rare; the Westinghouse proposal was chosen as the winner. At the time of that study, provisions realistically available for attitude updating consisted of mediocre-accuracy items such as magnetometers and horizon scanners– not bad but not spectacular either.
All that was of course before GPS weighed in, with its opportunity to reveal attitude from phase differences between antennas spaced at known distances apart. That vastly superior capability effectively reduced earlier crude measurements to relative obscurity. A directly parallel situation occurred in connection with navigation; the book that first tied together several facets of advancement in that field (integration, strapdown inertial, modern estimation with acceptance of all data sources, multimode operation, extension to tracking, clear exposition of all commonly used representations of attitude, etc.) was”pre-GPS” (1976), and consequently regarded as less relevant. Timing can be decisive — that’s no one’s fault.
The item just noted — attitude representation — is worth further discussion here. Unlike many other sources, the 1976 book offered an opportunity to use quaternion properties without any need to learn a specialized quaternion algebra. A literature search, however, will point primarily to various sources (of necessity, later than 1976).that benefit from the superior performance offered through GPS usage. Again, in view of GPS as a game-changer, that is not necessarily improper. Most publications on attitude determination don’t cite the first-ever investigation, sponsored by GSFC, for that innocent reason.
The word beginning that last sentence (“Most”) has an exception. One author, widely quoted as an authority (especially on quaternions), did cite the original work — dismissing it as “ad-hoc” — while using an exact copy of the sensitivity matrix elements pubished in my original investigation (the three references cited at the start of this blog).
While I obviously didn’t invent either quaternions or the Kalman filter, there was another thing I didn’t do: fail to credit, in my publications, pre-existing sources that contributed to my findings. Publication of the material cited here, I’ve been told, paved the way for understanding and insight to many who followed. No one owes me anything for that; an analyst’s work, truthfully and realistically presented, is what the analyst has to offer.
It is worth pointing out that both the attitude determination study and the 1976 book cover another facet of rotational analysis absent from many other related publications: dynamics — in the sense of physics. Whereas modern estimation lumps time-variations of the state together into one all-encompassing “dynamic” model, classical physics makes a separation: Kinematics defines the relation between position, rates, and accelerations. Dynamics determines translational accelerations resulting from forces or rotational accelerations resulting from torques.
Despite absence of GPS from my early (1960s/70s) investigations, one feature that can still make them useful for today’s analysts is the detailed characterization of torques acting — in very different ways — on spinning and gravity-gradient satellites, plus their effects on rotational motion. Many of the later studies focused on the rotational kinematics, irrespective of those torques and their consequences. Similarly, the “minimal-math”approach to explaining integrated navigation has enabled many to grasp the concepts. Printed testimony to that effect, from courses I taught decades ago, is augmented by more recent source noted near the end of another page shown on this site.
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).
Tracking acceleration dynamics by GNSS, radar, imaging
My 2007 book on GPS and GNSS (GNSS Aided Navigation & Tracking), as its title implies, involves both navigation and tracking. This discussion describes the latter, covered in the longest chapter of the book (Chapter 9). In addition to the flight-validated algorithms for navigation (processing of inertial sensor data, integration with GPS/GNSS, integrity, etc.), this text offers extensive coverage of tracking. Formulations are given for a variety of modes, in 2-D (e.g., for runway incursion prevention or ships) and 3-D (in-air), using GPS/GNSS and/or other sensors (e.g., radar, optical). Position and velocity vectors are formed, in some operations joined by some or all components of acceleration.
This author was fortunate to be “at-the-right-places at-the-right-times” when a need arose to address each of the topics covered. As a result, the words of one reviewer — that the book is
applies to tracking as well as to navigation. The book identifies subtleties that arise in specific applications (aircraft, ships, land vehicles, satellites, long-range or short-range projectiles, reentry vehicles, missiles, … ). In combination with a variety of possible conditions affecting sensor suite and location (air-to-air; air-to-ground; air-to-sea surface; surface-to-air, etc. — with measurements associated with distance or direction or both; shared or not shared among participants who may communicate from different positions), it is not surprising that striking contrasts can arise, influencing the characterization and approaches used. The array of formulations offered, while fully accounting for marked differences among operations, nevertheless exploits an underlying commonality to the maximum possible extent.
Tracking dynamics of aircraft, missiles, ships, satellites, projectiles, …
Formulations described in Chapter 9 were used for tracking of both aircraft and missiles, concurrently, through usage of an agile beam radar. For another example, air-to-surface operations subdivide into air-to-ground and vessel tracking from the air. That latter case constrains tracked objects’ altitudes to mean sea level — a substantial benefit since it obviates the need for elevation measurements, which are subject to large errors from refraction (bearing and range measurements, much less severely degraded, suffice). Air-to-ground tracking, by contrast, further subdivides into stationary and moving targets; the former potentially involves imaging possibilities (by real or synthetic aperture) while the latter — if not being imaged by inverse SAR — separates its signature from clutter via doppler.
Reentry vehicles, quite different from other track operations, present a unique set of “do’s” and “don’ts” owing to high-precision range measurements combined with much larger cross-range errors (because of proportionality to extreme distances involved). Pitfalls from uncertain axial direction of “pancake” shaped one-sigma error ellipsoids must be avoided. A counterexample, having angle observations only (without distance measurements), is also addressed. Orbit determination is unique in still another way, often permitting “patched-conic” modeling for its dynamics. A program based on Lambert’s theorem provides initial trajectories from two position vectors with the time interval separating them.
Those operations and more are addressed with most observations from radar or other (e.g., infrared imaging) sensors rather than satellite measurements. That of course applies to tracked objects carrying no squitters. Friendlies tracking one another, however, open the door for using GNSS data. Those subjects plus numerous supporting functions are discussed at some length in Chapter 9. Despite very different dynamics applicable to various operations, the underlying commonality (Chapter 2) connects the error propagation traits in their estimation algorithms and also — though widely unrecognized — short-term INS error propagation under cruise conditions (Chapters 2 and 5). Support operations such as synthetic aperture radar (SAR) and transfer alignment are described in the chapter Addendum.