A widespread missed opportunity began many years ago and continues to this day.  It is still widely believed that significant nonlinearity is inescapable in a tracker – whether for dynamics with spherical coordinates or for measurements with Cartesian coordinates.  The first half of that is definitely true for dynamics using the classical (range/elevation/azimuth) frame in air-to-air encounters at close range; we’ll take that issue first here.

One question that could be raised immediately might sound something line this: Since expressing dynamics in a range/elevation/azimuth frame causes so many problems (not only linearity but many more, to be discussed shortly), why even consider that as a candidate approach?  Old-timers will readily recall that analog radars provided no other choice.  They had range trackers, while angle tracking was done separately in outer loops with bandwidths narrow in comparison to inner stabilization loops maintained via antenna-mounted gyros.  Couldn’t that still be done after digitization?  Yes – in fact, it was done.  In the early 1970s I reviewed a paper for IEEE showing just that.  I gave it the green light because it was correct.  For my own design, though, I used a Cartesian frame (publication #24, 26, 28, 30, 32, 36, 60, 61, 66, and 69).  No contest.

The widely recognized nonlinear degradation of a range/elevation/azimuth representation for dynamics only begins to explain why that choice is fraught with problems.  For one issue, that loop-within-a-loop situation imposed a demand on inner stabilization bandwidth; if too low it would compromise the overall operation’s stability.   Alternatively that requirement could be viewed as a constraint on track loop responsiveness.  Another very serious issue was the interfacing requirements; gyro and accelerometer data had to be used in that track configuration (which added another burden of time-tagging plus another degradation from time-tag imperfections).  Still another limitation was inability to represent multiple track files; they aren’t all in the same direction and their Line-of-Sight rates are anything but uniform.  Finally, if handoff of a track file became necessary (e.g., from a forward-looking to a side-looking sensor during fly-by), I wouldn’t want to inherit that task with (range/elevation/azimuth) dynamics at close but wildly changing distances and geometries.

The item just noted brings up a favorite example raised by my coauthor of publication #24 and 32: Two aircraft approach each other on parallel tracks separated by 1000 ft.  With each having constant 1000 ft/sec groundspeed, the centripetal acceleration (see Ex. 8-12c on page 295 of Integrated Aircraft Navigation) at the instant of closest approach (sidelong position) is


or about 125 g.  The example is extreme but, even with more moderate encounters no range track loop can perform adequately in both responsiveness and noise rejection.  The second derivative of scalar distance is very high in close range scenarios.

Now a comparison to the Cartesian frame can begin.  Instantly the “problem” just shown disappears.  There isn’t any acceleration at all; all Cartesian velocity components are constant.  Then handoff is easy too.  We’re off to an excellent start.  Next: interfacing – that’s also easy – never mind the gyros and accelerometers, just adopt the INS nav frame as the Cartesian reference for tracking and use the nav computer output.  Eq. (2.13) of GNSS Aided Navigation and Tracking shows that it’s just as easy to track from a maneuvering fighter jet as it is while at rest.  Stabilization loop?  It isn’t inside any other loop; let it have whatever bandwidth it has.  Separate the stabilization offsets from tracker inputs as illustrated in Figure (9.2) of GNSS Aided Navigation and Tracking.  That same “dot-off-the-crosshairs” figure, with its accompanying analysis (Section 9.2.2), readily reduces to negligible levels any measurement nonlinearities as well.  Multiple targets?  Again, easy – just maintain one track file for each object being tracked.

That was fast, wasn’t it?

Low pass filter

Decisions are made, understandably, on the basis of a decision-maker’s beliefs.  In general, the better the knowledge base, the better the anticipated outcome.  Inevitably there are times when choices must be made from incomplete information.  Even that can still produce success, but the likelihood of a favorable outcome depends on recognition of those uncertainties.  Likelihood of an unfavorable outcome, then, increases when those information gaps go unrecognized.  That is, when we are unaware of the fact that we don’t know (“don’t-know-squared”).  To make that case for this site I’ll use an example from an area outside of navigation and tracking:

One field that has received thorough investigation is the study of a low-pass filter.  Users of those commonly believe that they know all that is needed to make the wisest design selection.  Quite often they know much – but not everything that would be useful to them.  It is not unusual for a maximally-flat (Butterworth) attenuation characteristic to be chosen while assuming that nothing much can be done about the accompanying nonlinear phase; latency often precludes usage of phase equalizers.  It is known – but not widely known – that a trade-off has been available for decades.  A near-linear phase characteristic over the passband can be realized if some of the attenuation requirements can be relaxed.  Full details can be found in

Handbook of Filter Synthesis by Anatol I. Zverev
ISBN 10: 0471986801 / 0-471-98680-1     ISBN 13: 9780471986805                                                           and
Filtering in the Time and Frequency Domains
by Herman J. Blinchikoff and Anatol I. Zverev
ISBN-10: 1884932177     ISBN-13: 978-1884932175

Already I’ve said as much as I intend to say here about low-pass filters.  To go this far without misinterpreting some points I found it necessary to consult a coauthor (Blinchikoff) of the second reference just cited.  The rest of the blogs on this site involve navigation and tracking – where avoidance of don’t-know-squared is still very much an issue.  Examples from those areas won’t all be obvious (e.g., a pilot believing his broken altimeter), but there is much to be gained from “looking under the hood” and uncovering missed opportunities.  If we’re willing to pursue that, let me assure you that vast improvements in performance are available.

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.