Most navigation performance definitions emphasize position. Important distinctions are wisely noted between error components (vertical versus horizontal, along-track versus cross-track) and criteria (absolute, relative, repeatable), but requirements often specify position while overlooking history. Attention to dynamics is warranted for interest in not only current but future position. Velocity accuracy is an important first addition. After a few examples, I’ll follow this reasoning for one, collision avoidance, to a logical conclusion.

The need to impose dynamics requirements is not universal. Position remains the primary consideration in some applications such as surveying, but counterexamples are more numerous. Take a hypothetical low-Earth orbiter, first coming into view of three terrestrial observers that are: widely separated (good trilateration geometry); coordinated, in tight communication, and synchronized; using scanning radars accurate in range only; and time-shared, with each object observed once per scan. Immediately upon processing the three suddenly appearing range measurements, a space object’s position is accurately known — but, with no orbit yet established, velocity error can be on the order of kilometers/second. Instantly, position accuracy changes from excellent to terrible.

Another spacecraft might approach the orbiter for rendezvous. Typically, a trim sequence is then conducted, reducing relative velocity to progressively smaller levels. Success obviously requires a final (at coupling initiation) low relative speed for both objects to withstand the soft impact. This operation clearly must account for velocity throughout.

Collision Avoidance. In-flight refueling also takes soft-collision velocity into account. In hard-collision control, however, dynamics often receive less thorough attention! “Position accuracy needed to avoid collision” is a common refrain. Criteria so expressed inevitably produce scenario-dependent solutions, likely affected by perceptions from limited insight and/or empirical evidence. To ensure safety despite widely varying conditions, incomplete concepts yield conservative decisions, and wider-than-necessary spacing in many cases.

I state a bottom line: correct evasions will be contingent on accurate knowledge of dynamics. A large error in estimating velocity could inhibit avoidance capability, contributing to a collision.

Occurrences of “position superb now, awful immediately after” depicted for a suddenly visible satellite are reminiscent of aircraft track files at radar lock-on. Initial accuracy can be fully adequate for position but not velocity. Doppler, if available, provides only along-range velocity. The cross-range component, perpendicular to that sightline, could be Mach 1, with East or West being equally likely. Thus 1,000 feet per second (fps) velocity error at acquisition is not farfetched. Controls devised to maintain the track file (for example, antenna steering; placement of gates to capture subsequent radar echoes from the same object) must initially cope. Slowness in driving velocity uncertainties down can cause signal loss, such as beam not illuminating the object, gates driven beyond Doppler and/or range cells holding the object’s response.

Even after range-rate uncertainty reduction, continuous Doppler gating needs repetitive velocity refresh. This is especially true for three-dimensional maneuvers and/or close range, where rapid geometry changes convert present cross-range motion into subsequent along-range motion.

One application clearly demanding attention to dynamics, landing on an aircraft carrier, requires continuous control of relative velocity. A still more general class of motion is thus coordinated: prescribed aircraft maneuvering accounts for ship’s rotation. Another maritime example: ships nearing coastlines restrict speed because of shoals and traffic densities.

For projectiles, cross-range target velocity estimation error produces a miss-distance contribution of order projectile flight time x cross-range velocity error, and flight time itself is in error by amounts commensurate with along-range velocity estimation error, producing miss-distance contributions of order projectile flight time error x cross-range velocity.

These examples are not exhaustive, but make the point: in different ways for different applications, knowledge of dynamics can be crucial. When velocity cannot fully define dynamics, extensions can include higher-order or more general effects, sucha as acceleration for tracking remote objects; verticality, drifts, and so on for navigation; rotations for coordinated relative motion between aircraft and aircraft carrier. Wide dynamic variations in some applications have prompted stipulation of more performance requirements such as settling time for reduction of velocity and higher-order errors within specified maxima.

Some (not all) operations account for dynamics, and often not in sufficient depth. Let’s look at aircraft on a collision course while airborne (in traffic collision avoidance system, or  TCAS) and on the ground (runway incursions). For this discussion, all encounters will be between an aircraft and an “intruder” — which may in fact be an intruder or anything from another aircraft to a truck or even a stationary object on a runway.

For collision avoidance, an intruder’s position is of course needed, but the key issue is separation distance at time of closest approach. To make that determination in a timely manner — well in advance of that closest approach time — clearly requires knowledge of dynamics. Velocity plays a direct role in determining both the time to closest approach and the projected miss distance at that time. When miss distance is below a specified amount (that is, aircraft or intruder size plus a safety margin exceeding the effects of estimation errors), guidance commands can be issued. In the airborne case (tomorrow’s horizontal TCAS modified to exploit accurate cross-range information), those commands could include evasive turns. To prevent incursions such as those involving aircraft on crossing runways, guidance commands could direct one vehicle to speed up, the other to slow down.

In both two-dimensional (runway) and three-dimensional (in-air) operation, closest approach time is not the familiar ratio of range to closing-range rate (time-to-go, which characterizes collision courses only). Recognition of this is evident in TCAS design, with conservative adjustments (DMOD) introduced for unknown cross-range motion at short distances. With more complete knowledge of velocity in cross-range as well as along-range, the conservatism can be eliminated without compromising safety.

Current plans for collision avoidance preceded GPS and the commitment to use it for commercial aviation. I have since described a way to determine velocity at high accuracy in all three dimensions, using GPS to full effectiveness, in “Send Measurements, not Coordinates,” ION Journal, Fall 1999. Although I have emphasized here one aspect of performance (accuracy), consideration of dynamics affects other criteria. Integrity tests have successfully been applied to velocity information, and credible velocity histories can enable continued operation during brief data blackouts.

In view of recent events, no serious proposal to use GNSS can ignore backup, especially where safety is involved. For occasional unavailability of GNSS, just use existing provisions. At most times in most places, enough GNSS information will be present to direct the function and vastly improve performance.

Terry’s column and recent initiatives such as PNT architecture of the future highlight a significant need: better and broader information for the departments of Transportation and Defense. What’s to be done? Again, the McGurn prescription: (1) ask the right questions and (2) provide answers. If industry won’t support that, we’ll repeat the past: performance deficiencies and, despite economical devices, uncontrolled system costs. That’s no exaggeration; there’s much at stake. My book GNSS-Aided Navigation and Tracking (2007, NavtechGPS) discusses ways to provide the right information, at both input and output, with special attention to robustness.

Carrier phase, under siege from interference, scintillation, masking, obscuration, and so on, can be everywhere ambiguous, repeatedly interrupted — and still fully exploited.

Worth repeating: better and broader information for DoT and DoD. Let’s really follow through this time.

JAMES L. FARRELL worked for 31 years at Westinghouse in design, simulation, and validation of navigation and tracking programs. He continues teaching and consulting for private industry, the DoD, and university research through Vigil, Inc.