Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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Symbols × vector cross product • dot product, scalar product euclidian norm, 2-norm, length of a vector ∂ partial derivative α angle between satellite velocity and satellite-to-user vector △f frequency measurement error caused by receiver clock drift △n vector n estimate correction in an iterative algorithm △t receiver time estimate bias △ti signal propagation time from the ith satellite △wu error in user velocity vector estimate △x vector x estimate correction in an iterative algorithm ɛ machine precision ɛ ˙ρ delta range vector measurement noise ɛρi measurement noise of pseudorange from the ith satellite ɛ ˙ρi measurement noise of delta range from the ith satellite ɛd clock drift equivalent error ɛfi satellite i frequency measurement error ɛru user position error ɛx positioningerror vector ν1,ν2 degrees of freedom ω transmitted frequency ω ′ received frequency θ angle between relative velocity and wave propagation direction ˙ρ delta range measurement vector ˆρ expected pseudorange vector ˆ˙ρ expected delta range vector ρi pseudorange measurement from the ith satellite ˙ρi delta range measurement from the ith satellite ˆρi expected pseudorange from the ith satellite ˙ρ T true delta range vector ρTi true pseudorange from the ith satellite ˙ρTi true delta range from the ith satellite σ standard deviation ix
σ2 variance, covariance a vector in R3 ai relative acceleration vector of the ith satellite with respect to the user A Doppler geometric dilution of precision matrix b vector in R3 c speed of light c vector in R3 cov covariance operator d receiver clock drift equivalent, derivative ˆd estimated receiver clock drift equivalent Di Doppler shift from the ith satellite E expectation value operator f real valued function f(ɛx) probability distribution function of positioningerror vector fi measured frequency from satellite i g real valued function G Doppler geometry matrix H pseudorange geometry matrix I identity matrix i, j, k, l satellite indexes L1 GPS civil frequency 1575.42 MHz L2 GPS military frequency 1227.6 MHz n number of satellites used in the calculations n user position and time vector ˆn estimated user position and time vector p(ˆx) delta range residuals function pi(ˆx) ith component of delta range residuals function R set of real numbers ri satellite i position vector ru user position vector ˆru estimated user position vector T matrix transpose tu receiver clock bias ˙tu receiver clock drift v speed vprop wave propagation speed vrel transmitter relative speed with respect to the receiver vi estimated satellite i relative velocity vector with respect to the user wi satellite i velocity vector wTu true user velocity vector wu estimated user velocity vector x wave transmitter position x user position and drift vector ˆx estimated user position and drift vector initial guess for user position and drift vector x0 x
Page 1 and 2: TAMPERE UNIVERSITY OF TECHNOLOGY De
Page 3 and 4: Contents Abstract v Tiivistelmä vi
Page 5 and 6: 5.2.3 Applications of the Doppler D
Page 7 and 8: Tiivistelmä TAMPEREEN TEKNILLINEN
Page 9: Abbreviations and Acronyms C/A coar
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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