Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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3.4 PositioningErrorAnalysis ...................... 13 3.5 LimitationsoftheGPS........................ 14 4 Doppler Positioning with the GPS 16 4.1 NeedforDopplerPositioning..................... 16 4.2 ComparisonbetweenGPSandTransit ............... 17 4.3 TheGoverningEquations ...................... 18 4.3.1 TheDopplerShiftEquation ................. 18 4.3.2 TheClockDriftError .................... 20 4.3.3 Mathematical Problem Formulation . . . . . . . . . . . . . 21 4.4 SymbolicMethods .......................... 23 4.4.1 Solvingthe Receiver Position . . . . . . . . . . . . . . . . 23 4.4.2 Existence and Uniqueness Considerations . . . . . . . . . . 23 4.5 StandardNumericalMethods .................... 24 4.5.1 ProblemFormulation..................... 24 4.5.2 TheNewtonMethod ..................... 25 4.5.3 TheGauss-NewtonMethod ................. 26 4.5.4 CalculatingtheDerivativeMatrix.............. 27 4.6 ProblemSpecificIterativeMethods ................. 30 5 Positioning Performance 31 5.1 MeasurementNoise.......................... 31 5.1.1 IonosphericEffects ...................... 31 5.1.2 Receiver Noise . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.1.3 UnknownUserVelocity.................... 32 5.1.4 BiasedTimeEstimate .................... 34 5.2 PositioningAccuracy......................... 35 5.2.1 Effect of Measurement Errors on PositioningSolution . . . 35 5.2.2 Doppler Dilution of Precision . . . . . . . . . . . . . . . . 36 iii
5.2.3 Applications of the Doppler Dilution of Precision Concept 39 5.3 Case of Normally Distributed Measurement Noise . . . . . . . . . 40 6 Numerical Results 43 6.1 MeasurementData .......................... 43 6.2 PropertiesoftheMeasurementNoise ................ 44 6.2.1 Hypothesis of the Properties of the Measurement Errors . 44 6.2.2 Numerical Testingof Normality . . . . . . . . . . . . . . . 45 6.2.3 Numerical Testingof Correlation . . . . . . . . . . . . . . 45 6.2.4 MagnitudeofErrors ..................... 47 6.2.5 Conclusions .......................... 48 6.3 PositioningPerformancewithRealData .............. 48 6.3.1 PositioningAccuracy..................... 48 6.3.2 Convergence.......................... 50 6.4 PositioningPerformance with Simulated Data.................................. 50 6.4.1 PositioningAccuracy..................... 51 6.4.2 TheDistributionofDPDOPValues............. 51 7 Conclusions 53 iv
Page 1 and 2: TAMPERE UNIVERSITY OF TECHNOLOGY De
Page 3: Contents Abstract v Tiivistelmä vi
Page 7 and 8: Tiivistelmä TAMPEREEN TEKNILLINEN
Page 9 and 10: Abbreviations and Acronyms C/A coar
Page 11 and 12: σ2 variance, covariance a vector i
Page 13 and 14: Chapter 1 Introduction Satellite po
Page 15 and 16: Chapter 2 The Doppler Effect In thi
Page 17 and 18: in Figure 2.2. The shape of the so
Page 19 and 20: Chapter 3 The Global Positioning Sy
Page 21 and 22: sufficiently many satellites, the r
Page 23 and 24: The satellite signal is very accura
Page 25 and 26: The estimated position and time vec
Page 27 and 28: in weak signal conditions. The key
Page 29 and 30: navigation message. Here, however,
Page 31 and 32: where wi is the satellite velocity,
Page 33 and 34: the receiver clock is runningfast a
Page 35 and 36: Let us now turn into our main goal,
Page 37 and 38: Definition 3. Delta range residuals
Page 39 and 40: method [Fletcher, p. 110], [Kaleva1
Page 41 and 42: product formula a × (b × c) =(a
Page 43 and 44: Chapter 5 Positioning Performance I
Page 45 and 46: eplaced by vi −△wu. Let us rewr
Page 47 and 48: Thus, the time bias effect to the p
Page 49 and 50: Let us first calculate the expected
Page 51 and 52: • Doppler drift dilution of preci
Page 53 and 54: Let us now make the even stronger a
Page 55 and 56:
Chapter 6 Numerical Results In Chap
Page 57 and 58:
6.2.2 Numerical Testing of Normalit
Page 59 and 60:
6.2.4 Magnitude of Errors The actua
Page 61 and 62:
Histogram of positioning errors wit
Page 63 and 64:
used for testinghow the algorithm b
Page 65 and 66:
Chapter 7 Conclusions This thesis d
Page 67 and 68:
The positioningalgorithm was develo
Page 69 and 70:
[Hill] Hill, Jonathan. The Principl
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Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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