1998 - Draper Laboratory

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BiographyRichard Phillips is a Principal Member of the Technical Staff in the Guidance and TechnologyDivision at Draper. He has worked at Draper for more than 25 years, principally in the areas ofguidance and navigation of spacecraft and aircraft. He received a BS degree in Physics from theMassachusetts Institute of Technology and a PhD degree in Physics from Tufts University.e-mail: rphillips@draper.comRichard PhillipsRelative and Differential GPS Data Transfer and Error Analysis / Biography1
Relative and Differential GPSData Transfer and ErrorAnalysisRichard Phillips The Charles Stark Draper Laboratory, Inc.Based on the paper published in the Proceedings of the 1997 53rd Annual ION MeetingAbstractIn this study, the distinction is made between Relative GlobalPositioning System (RGPS) and Differential GPS (DGPS). Boththese terms imply a transfer of information from a referencereceiver to an active receiver. Expressions for the errorsassociated with three different data transfer “formats” are derived.A numerical evaluation of the errors associated with one of theseformats is made.It is often stated that the DGPS reference receiver must be placedat a known location. It can be a major effort to survey such alocation accurately. In the final analysis, it is never perfectlyknown, and location errors play a role in the resulting DGPSperformance. This is in contrast to the RGPS strategy, whichadmits that surveying errors exist, but ensures that they arecorrelated between reference receiver and target. With the RGPSconcept, it is only necessary to know the target location relative tothe reference receiver. These data can be obtained in a number ofways, such as from existing maps that are accurate in a relativesense, but with a relationship to a global coordinate system that ispoorly known. Synthetic Aperture Radar (SAR) target locationalso yields coordinates for points that are well known relative toone another, but with an absolute location that may not be so wellknown. Such relative data might also come from instruments thatmeasure the target position with respect to the reference receiver.Hand-held ranging/direction-finding devices are an example ofsuch instruments. In the first two examples, the primarymeasurements are of two locations. In the latter example, theprimary measurements are of a single location and the vector fromthat location to another.Two major sources of error are the difference in GPS bias errorsbetween reference receiver and active receiver and the differencein mapping error between reference receiver and target. Althoughthe relative GPS information can be transferred by one of threemethods, it will be shown that there are first-order differences thatdepend on receiver separation distance. The proper transferformat in any situation is a function of this error as well aslogistical considerations.It will be seen that it is possible to do relative GPS target locationusing pseudorange bias transfer to an active receiver that can seeonly a subset of the satellites in view at the reference receiver.This fact makes the logistics of relative targeting easier than if thetarget coordinates were to be computed and transmitted. Rapidlocation of a relocatable target provides a good example. Anunattended reference station/SAR transponder can be airdroppedinto place near the target area. It is immediately followed by aSAR reconnaissance aircraft that images and defines coordinatesfor both the reference station and targets. The reconnaissanceaircraft in turn is closely followed by GPS-guided weapons thatreceive target coordinates from the reconnaissance aircraft andpseudorange bias corrections from the reference receiver. Thesebias corrections compensate for both pseudorange errors and(absolute) SAR survey errors. It is not necessary to computecoordinates for each target based on the current referencereceiver reading. Simply broadcasting the pseudorange biascorrections suffices. Each weapon uses these bias corrections (ora subset of them) and the coordinates of its designated targetdetermined once by the reconnaissance aircraft.The error on target incurred by using pseudorange biases forrelative GPS targeting was computed for several latitudes, for tworeceiver separation distances, and for both four and eight satellitesignals in lock at the active receiver. For all latitudes, thehorizontal error is about 0.5 m at a 500-km separation and 1.1 mat a 1000-km separation.AnalysisFigure 1 shows the location of the reference receiver, the activereceiver, and the target at the instant of weapon impact. Thereference receiver is on the right; the active receiver and the targetare on the left. The reference receiver is at the true location. Wemust presume it is at the surveyed location, and GPS indicatesthat it is at the GPS location. The target is at the true targetposition, but to the best of our knowledge, it is at the surveyedlocation. The active receiver (the one on the weapon), “thinks” itRelative and Differential GPS Data Transfer and Error Analysis2
Page 2 and 3: Letter from thePresident and CEO,Vi
Page 4 and 5: Information TechnologyMilton AdamsE
Page 6 and 7: BiographyMilton Adams has been at D
Page 9 and 10: Figure 1 represents a functional de
Page 11 and 12: Programs. In effect, these controll
Page 13 and 14: Although the terminal area traffic
Page 15 and 16: Table 2. ATFM performance evaluatio
Page 17 and 18: In the experiments, a nominal capac
Page 19 and 20: [3] Wambsganss, Michael C. “Colla
Page 21 and 22: Guidance, Navigation, and Control A
Page 23 and 24: A Control Lyapunov FunctionApproach
Page 25 and 26: x( 0) ∈ X and w(t) ∈Wfor all t
Page 27 and 28: (b) Select a quadratic RCLF V i (x)
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Page 31 and 32: References[1] Ball, J.A. and A.J. v
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Page 37 and 38: The first term on the right in the
Page 39 and 40: H R# δρ R,GPS -H A# δρ A,GPSThi
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Page 45 and 46: Segmentation of MR ImagesUsing Curv
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Page 49 and 50: Experimental ResultsThe results of
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Page 55 and 56: BiographyGeorge SchmidtGeorge Schmi
Page 57 and 58: clock and ephemeris errors, as well
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Page 63 and 64: performed, then the target location
Page 65 and 66: tightly-coupled system, however, ca
Page 67 and 68: Concluding RemarksRecent progress i
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anomaly M and/or the ascending node
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However, since optimization and rec
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is maintained in the Northern Hemis
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autonomy. It must have the ability
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[31] Neelon, Joseph G., Jr., Paul J
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Draper’s primary goal is to Drape
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)Rotordynamic Modelingof an Activel
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Eq. (9) becomes:λ[ R ] { Φ } = [
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chosen to be 24, for a total of 48
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InertialInstruments/MechanicalDesig
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BiographyJeffrey Borenstein is curr
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process step. Process information i
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Figure 4. Control chart for boron d
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References[1] Barbour, N., J. Conne
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Draper Laboratory continues to engi
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Validating the Validating Tool:Defi
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calculates miscellaneous terms, suc
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Table 1. Suggested specification sh
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User Accuracy as aFunction of Simul
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20-min averaging, this clock lockin
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Table 2. Sample high-level summary
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AcknowledgmentR.L. Greenspan, J.A.
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Systems IntegrationRich MartoranaPe
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BiographyAnthony Kourepenis is an A
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control is employed to maintain the
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Table 1. Summary of automotive yaw
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Resolution (60 Hz) deg/h10000000100
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References[1] Greiff, P., B. Boxenh
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Guidance, Navigation, and Control A
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An Integrated Safety AnalysisMethod
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Infrastructure ModelsSystemRequirem
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Figures 6 and 7 illustrate the bloc
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Notice that each flight track descr
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Table 7. Safety statistics at 1700-
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Guidance, Navigation, and Control A
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An Optimal Guidance Law forPlanetar
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Note that the states in the three d
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Crossrange (Kft)10090807060504030Cl
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The 1997 Charles StarkDraper PrizeT
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The 1997 Charles StarkDraper Prize1
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“Draper encourages its personnel
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Gimballed Vibrating GyroscopeHaving
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Optical Source Isolator withPolariz
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Hunting Suppressor forPolyphase Ele
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Sensor Having an Off-Frequency Driv
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proof mass from transients and enha
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1997 Published PapersThe following
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monitoring of space structures and
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measured by kinematic degrees of fr
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i.e., what percent of the earth’s
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McConley, M. W.; Dahleh, M. A.; Fer
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unaffordable, or even misguided. Bu
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The Draper DistinguishedPerformance
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Educational Activitiesat Draper Lab
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1998 - Draper Laboratory

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