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 Shortcomings in all four areas are made more severe by continuation of outdated methods, as unnecessary as they are fundamental, Not everyone wants to hear this but it’s self-evident: conformance to custom — using decades-old design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 comment challenged my video .  I’m glad it included an acknowledgment that some points might have been missed. To be frank that happened a bunch; bear with me while I explain. First, there’s the accuracy issue; doppler &/or deltarange info provided from many receivers is far less accurate than carrier phase (sometimes due to cutting corners in implementation — recall that carrier phase, as the integral of doppler, will be smoother if processing is done carefully). Next, preference for 20-msec intervals will backfire badly. If phase noise at L-band gives a respectable 7mm = 0.7cm, doppler velocity error [(current phase) – (previous phase)] / 1 sec is (1.414) (0.7) = 1 cm/sec RMS for a 1-sec sequential differencing interval.  Now use 20 msec: FIFTY times as much doppler error! Alternatively if division is implicit instead of overt, degradation is more complicated: sequential phase differences are highly correlated (with a correlation coefficient of -1/2, to be precise). That’s because the difference (current phase) – (previous phase) and the difference (next phase) – (current phase) both contain the common value of current phase. In a modern estimation algorithm, observations with sequentially correlated errors are far more difficult to process optimally.  That topic is a very deep one; Section 5.6 and Addendum 5.B of my 2007 book address it thoroughly. I’m not expecting everyone to go through all that but, to offer fortification for its credibility, let me cite a few items:

* agreement from other designers who abandoned efforts to use short intervals
* table near the bottom of a page on this site.

* phase residual plots from Chapter 8 of my 2007 book.

The latter two, it is recalled, came from flight test for an extended duration (until flight recorder was full), under severe test aircraft (DC-3) vibration.

For doppler updating from sources other than satnav, my point is stronger still. Doppler from radar (which lacks the advantage of passive operation) won’t get velocity error much below a meter/sec — and even that is an improvement over unaided inertial nav (we won’t see INS velocity specs expressed in cm/sec within our lifetime).

Additional advantages of what the video offers include (1) no requirement for a mask angle (2) GNSS interoperability, and (3) robustness. A brief explanation:

(1) Virtually the whole world discards all measurements from low-elevation satellites because of propagation errors. But ionospheric and tropospheric effects change very little over a second; 1-sec phase differences are great for velocity information. Furthermore they offer a major geometry advantage while occurrence of multipath would stick out like a sore thumb, easily edited out.
(2) 1-sec differences from various constellations are much easier to mix than the phases themselves. 
(3) For receivers exploiting FFT capability  even short fragments of data, not sufficiently continuous for conventional mechanizations (track loops), are made available for discrete updates.
The whole “big picture” is a major improvement is robust operation 

The challenger isn’t the only one who missed these points; much of our industry, in fact, is missing the boat in crucial areas. Again I understand skepticism, but consider the “conventional wisdom” regarding ADSB: Velocity errors expressed in meters per second — you can hear speculative values as high as ten. GRADE SCHOOL ARITHMETIC shows how scary that is; collision avoidance extrapolates ahead. Consider the vast error volume resulting from doing that 90 seconds ahead of closest approach time with several meters per second of velocity error. So — rely on see-and-avoid? There are beaucoup videos that show how futile that is (and many more videos that show how often near misses occur — in addition there are about a thousand runway incursions each year). That justifies the effort for dramatic reduction of errors in tracking dynamics — to cm/sec relative velocity accuracy.

It’s perfectly logical for people to question my claims if they seem too good to be true. All I ask is follow through, with visits to URLs cited here.

GPS Carrier Phase for Dynamics ?

The practice of dead reckoning (a figurative phrase of uncertain origin) is five centuries old.   In its original form, incremental excursions were plotted on a mariner’s chart using dividers for distances, with directions obtained via compass (with corrections for magnetic variation and deviation). Those steps, based on perceived velocity over known time intervals, were accumulated until a correction became available (e.g., from a landmark or a star sighting).

Modern technology has produced more accurate means of dead reckoning, such as Doppler radar or inertial navigation systems.   Addressed here is an alternative means of dead reckoning, by exploiting sequential changes in highly accurate carrier phase. The method, successfully validated in flight with GPS, easily lends itself to operation with satellites from other GNSS constellations (GALILEO, GLONASS, etc.).  That interoperability is now one of the features attracting increased attention; sequential changes in carrier phase are far easier to mix than the phases themselves, and measurements formed that way are insensitive to ephemeris errors (even with satellite mislocation,  changes in satellite position are precise).

Even with usage of only one constellation (i.e., GPS for the flight test results reported here), changes in carrier phase over 1-second intervals provided important benefits. Advantages to be described now will be explained in terms of limitations in the way carrier phase information is used conventionally.   Phase measurements are normally expressed as a product of the L-band wavelength multiplied by a sum in the form (integer + fraction) wherein the fraction is precisely measured while the large integer must be determined. When that integer is known exactly the result is of course extremely accurate.  Even the most ingenious methods of integer extraction, however, occasionally produce a highly inaccurate result.   The outcome can be catastrophic and there can be an unacceptably long delay before correction is possible.   Elimination of that possibility provided strong motivation for the scheme described here.

Linear phase facilitates streaming velocity with GNSS interoperability

With formation of 1-sec changes, all carrier phases can be forever ambiguous, i.e., the integers can remain unknown; they cancel in forming the sequential differences. Furthermore, discontinuities can be tolerated; a reappearing signal is instantly acceptable as soon as two successive carrier phases differ by an amount satisfying the single-measurement RAIM test.   The technique is especially effective with receivers using FFT-based processing, which provides unconditional access, with no phase distortion, to all correlation cells (rather than a limited subset offered by a track loop).

Another benefit is subtle but highly significant: acceptability of sub-mask carrier phase changes. Ionospheric and tropospheric timing offsets change very little over a second. Conventional systems are designed to reject measurements from low elevation satellites. Especially in view of improved geometric spread, retention here prevents unnecessary loss of important information.   Demonstration of that occurred in flight when a satelllite dropped to horizon; submask pseudoranges of course had to be rejected, but all of the 1-sec carrier phase changes were perfectly acceptable until the satellite was no longer detectable.

One additional (deeper) topic, requiring much more rigorous analysis, arises from sequential correlations among 1-sec phase change observables. The issue is thoroughly addressed and put to rest in the later sections of the 5th chapter of GNSS Aided Navigation and Tracking.

Dead reckoning capability without-IMU was verified in flight, producing decimeter/sec RMS velocity errors outside of turn transients (Section 8.1.2, pages 154-162 of the book just cited). With a low-cost IMU, accuracy is illustrated in the table near the bottom of a 1-page description on this site (also appearing on page 104 of that book). All 1-sec phase increment residual magnitudes were zero or 1 cm for the seven satellites (six across-SV differences) observed at the time shown. Over almost an hour of flight at altitude (i.e., excluding takeoff, when heading uncertainty caused larger lever-arm vector errors), cm/sec RMS velocity accuracy was obtained.

GPS codes are chosen to produce a strong response if and only if a received signal and its anticipated pattern are closely aligned in time. Conventional designs thus use correlators to ascertain that alignment. Mechanization may take various forms (e.g., comparison of early-vs-late time-shifted replicas), but dependence on the correlation is fundamental. There is also the complicating factor of additional coding superimposed for satellite ephemeris and clock information but, again, various methods have long been known for handling both forms of modulation. Tracking of the carrier phase is likewise highly developed, with capability to provide sub-wavelength accuracies.

An alternative approach using FFT computation allows replacement of all correlators and track loops. The Wiener-Khintchine theorem is well over a half-century old (actually closer to a century), but using it in this application has become feasible only recently. To implement it for GPS a receiver input’s FFT is followed with term-by-term multiplication by the FFT of each separate anticipated pattern (again with optional insertion of fractional-millisecond time shifts for further refinement and again with various means of handling the added clock-&-ephemeris modulation). According to Wiener-Khintchine, multiplication in the frequency domain corresponds to convolution in time — so the inverse FFT of the product provides the needed correlation information.

FFT processing instantly yields a number of significant benefits. The correlations are obtained for all cells, not just the limited few that would be seen by a track loop. Furthermore all cell responses are unconditionally available. Also, FFTs are not only unconditionally stable but, as an all-zero filter bank (as opposed to a loop with poles as well as zeros), the FFT provides linear phase in the passband. Expressed alternatively, no distortion in the phase-vs-frequency characteristic means constant group delay over the signal spectrum.

The FFT processing approach adapts equally well with or without IMU integration. With it, the method (called deep integration here) goes significantly beyond ultratight coupling, which was previously regarded as the ultimate achievement. Reasons for deep integration’s superiority are just the traits succinctly noted in the preceding paragraph.

Finally it is acknowledged that this fundamental discussion touches very lightly on receiver configuration, only scratching the surface. Highly recommended are the following sources plus references cited therein:

* A very early analytical development by D. van Nee and A. Coenen,
“New fast GPS code-acquisition techniquee using FFT,” Electronics Letters, vol. 27, pp. 158–160, January 1991.

* The early pioneering work in mechanization by Prof. Frank van Graas et. al.,
“Comparison of two approaches for GNSS receiver algorithms: batch processing and sequential processing considerations,” ION GNSS-2005

* the book by Borre, Akos, Bertelsen, Rinder, and Jensen,
A software-defined GPS and Galileo receiver: A single-frequency approach (2007).

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.