Chapter 5 GPS Absolute Positioning Determination …

1 EM 1110-1-10031 Aug 96 Chapter 5 GPS Absolute Positioning DeterminationConcepts, Errors, and Accuracies5-1. GeneralNAVSTAR GPS Determination of a point position on theearth actually uses techniques common to conventionalsurveying trilateration:an electronic distance measure-ment resection. The user s receiver simply measures thedistance ( , ranges) between the earth and theNAVSTAR GPS satellite(s). The user s position is deter-mined by the resected intersection of the observed rangesto the satellite range creates a spherewhich forms a circle (approximately) upon intersectionwith the earth s surface. Given observed ranges to twodifferent satellites, two intersecting circles result fromwhich a horizontal (2D) position on the earth can a third satellite range creates threespheres, the intersection point of which will provide theX-Y-Z geocentric coordinates of a point.

2 Adding moresatellite ranges will provide redundancy in the Positioning ,which allows adjustment. In actual practice, at least foursatellite observations are required in order to resolvetiming variations for a 3D Absolute PositioningAbsolute Positioning involves the use of only a singlepassive receiver at one station location to collect datafrom multiple satellites in order to determine the station slocation. It is not sufficiently accurate for precise survey-ing or hydrographic Positioning uses. It is, however, themost widely used military and commercial GPS position-ing method for real-time navigation and location (seeparagraph 2-1b). accuracies obtained by GPS Absolute posi-tioning are dependent on the user s user can obtain real-time point positional accuraciesof 100 m.

3 The lower level of accuracies achievable usingSPS is due to intentional degradation of the GPS signalby the DoD (S/A).The PPS user (usually a DoD-approved user) can use a decryption device to achieve apoint positional (3D) accuracy in the range of 10-16 mwith a single-frequency receiver . Accuracies to less thana meter can be obtained from Absolute GPS measurementswhen special equipment and post-processing techniquesare Absolute point Positioning with the carrier using broadcast ephemerides, the user is able to usepseudo-range values in real time to determine absolutepoint positions with an accuracy of between 3 m in thebest of conditions and 80 m in the using apost-processed ephemerides ( , precise), the user canexpect Absolute point positions with an accuracy of near1 m in the best of conditions and 40 m in the Pseudo-RangingWhen a GPS user performs a GPS navigation solution,only an approximate range, or pseudo-range, to selectedsatellites is measured.

4 In order for the GPS user to deter-mine his/her precise location, the known range to thesatellite and the position of those satellites must pseudo-ranging, the GPS user measures anapproximate distance between the antenna and the satelliteby correlation of a satellite-transmitted code and a refer-ence code created by the receiver , without any correctionsfor errors in synchronization between the clock of thetransmitter and that of the distance thesignal has traveled is equal to the velocity of the transmis-sion of the satellite multiplied by the elapsed time oftransmission, with satellite signal velocity changes due totropospheric and ionospheric conditions being to Figure 5-1 for an illustration of the pseudo-rang-ing concept.

5 (See also paragraph 2-4a,b.)a. The accuracy of the positioned point is a functionof the range measurement accuracy and the geometry ofthe satellites, as reduced to spherical intersections with theearth s surface. A description of the geometrical magnifi-cation of uncertainty in a GPS-determined point positionis Dilution of Precision (DOP), which is discussed insection 5-6d(2).Repeated and redundant range obser-vations will generally improve range accuracy. However,the dilution of precision remains the a staticmode (meaning the GPS antenna stays stationary), rangemeasurements to each satellite may be continuouslyremeasured over varying orbital locations of the satel-lite(s).The varying satellite orbits cause varying posi-tional intersection addition, simultaneousrange observations to numerous satellites can be adjustedusing weighting techniques based on the elevation andpseudo-range measurement pseudo-range observations are needed toresolve a GPS 3D position.

6 (Only three pseudo-rangeobservations are needed for a 2D location.) In practicethere are often more than four. This is due to the need to5-1EM 1110-1-10031 Aug 96 Figure 5-1. GPS satellite range measurementresolve the clock biases tcontained in both the satelliteand ground-based , in solving for theX-Y-Z coordinates of a point, a fourth unknown ( ,clock bias) must also be included in the of the 3D position of a point is simply the solu-tion of four pseudo-range observation equations contain-ing four unknowns, , X, Y, Z, and A pseudo-range observation is equal to the truerange from the satellite to the user tplus delays due tosatellite/ receiver clock biases and other effects, as wasshown in Figure 5-1.(5-1)Rptc( t)dwhereR= observed pseudo-range t= true range to satellite (unknown)c= velocity of propagation t= clock biases ( receiver and satellite)d= propagationdelaysduetoatmosphericconditi onsThese are usually estimated from true range tis equal to the 3D coordinate differencebetween the satellite and user.

7 (5-2) t(XsXu)2(YsYu)2(ZsZu)212whereXs,Ys,Zs= knownsatellitecoordinatesfromephemeris dataXu,Yu,Zu= unknown coordinates of user which are tobe four pseudo-ranges are observed, four equations areformed from Equations 5-1 and 5-2.(5-3)R1c td12Xs1Xu2Ys1Yu2Zs1Zu2(5-4)R2c td22Xs2Xu2Ys2Yu2Zs2Zu25-2EM 1110-1-10031 Aug 96(5-5)R3c td32Xs3Xu2Ys3Yu2Zs3Zu2(5-6)R4c td42Xs4Xu2Ys4Yu2Zs4Zu2In these equations, the only unknowns areXu,Yu,Zu, and t. Solving these equations at each GPS update yields theuser s 3D position more pseudo-range observations provides redundancy to the instance, if seven satellites are simultaneouslyobserved, seven equations are derived, and still only fourunknowns solution is highly dependent on the accuracyof the known coordinates of each satellite ( ,Xs,Ys, andZs), the accuracy with which the atmospheric delaysdcanbe estimated through modeling, and the accuracy of theresolution of the actual time measurement process per-formed in a GPS receiver (clock synchronization, signalprocessing, signal noise, etc.)

8 As with any measurementprocess, repeated and long-term observations from asingle point will enhance the overall positional GPS Error SourcesThere are numerous sources of measurement error thatinfluence GPS performance. The sum of all systematicerrors or biases contributing to the measurement error isreferred to as range bias. The observed GPS range, with-out removal of biases, is referred to as a biased range or pseudo-range. Principal contributors to the final rangeerror that also contribute to overall GPS error are epheme-ries error, satellite clock and electronics inaccuracies,tropospheric and ionospheric refraction, atmosphericabsorption, receiver noise, and multipath include those induced by DoD (Selective Availabil-ity (S/A) and Anti-Spoofing (A/S)).

9 In addition to thesemajor errors, GPS also contains random observationerrors, such as unexplainable and unpredictable time vari-ation. These errors are impossible to model and following paragraphs discuss errors associated withabsolute GPS Positioning of these errorsare either eliminated or significantly minimized whenGPS is used in a differential mode. This is due to thesame errors being common to both receivers during simul-taneous observing sessions. For a more detailed analysisof these errors, consult one of the technical referenceslisted in Appendix errors and orbit ephemeris errors are errors in the prediction of asatellite position which may then be transmitted to theuser in the satellite data message.

10 Ephemeris errors aresatellite dependent and very difficult to completely correctand compensate for because the many forces acting on thepredicted orbit of a satellite are difficult to measuredirectly. Because direct measurement of all forces actingon a satellite orbit is difficult, it is nearly impossible toaccurately account or compensate for those error sourceswhen modeling the orbit of a previousaccuracy levels stated are subject to performance ofequipment and errors produceequal error shifts in calculated Absolute point relies very heavily on accu-rate time satellites carry rubidiumand cesium time standards that are usually accurate to1 part in 1012and 1 part in 1013, respectively, while mostreceiver clocks are actuated by a quartz standard accurateto 1 part in 108.