GPS World - February 2008 - (Page 8)

EXPERT ADVICE Accuracy in More than Position Only James L. Farrell T erry McGurn’s closing observations in his November 2007 column on accuracy evoke a grateful reaction from me. Glib summaries of performance are incomplete. Pinpointing moving objects within ever-smaller fractions of size is not always most important; frequently, it’s knowing where they’ll be a little later. 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, repeat- Requirements often specify position while overlooking history. able), 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. e 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. is 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-thannecessary 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. e cross-range component, perpendicular to that sightline, could be Mach 1, with East or West being equally likely. us 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. is 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 missdistance contribution of order projectile ﬂight time cross-range velocity error, and ﬂight time itself is in error by amounts commensurate with along-range velocity estimation error, producing missdistance contributions of order projectile ﬂight time error cross-range velocity. ese 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 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, DoD, and university research through Vigil, Inc. 8 GPS World | February 2008 www.gpsworld.com http://www.gpsworld.com

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GPS World - February 2008 Contents Out in Front Expert Advice Galileo's Second Coming Soon UPS First to Use ADS-B European Industry Group Galileo Validation 2008 Antenna Survey Tsumani Detection by GPS Classifieds Advertisers Index Seen + Heard

GPS World - February 2008

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