The GNSS integer ambiguities: estimation and validation

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Teunissen PJG (1995). The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70: 65–82. Teunissen PJG (1997). A canonical theory for short GPS baselines. Part IV: Precision versus reliability. Journal of Geodesy, 71: 513–525. Teunissen PJG (1998a). A class of unbiased integer GPS ambiguity estimators. Artificial Satellites, 33(1): 4–10. Teunissen PJG (1998b). GPS carrier phase ambiguity fixing concepts. In: PJG Teunissen and A Kleusberg, GPS for Geodesy, Springer-Verlag, Berlin. Teunissen PJG (1998c). On the integer normal distribution of the GPS ambiguities. Artificial Satellites, 33(2): 49–64. Teunissen PJG (1998d). Success probability of integer GPS ambiguity rounding and bootstrapping. Journal of Geodesy, 72: 606–612. Teunissen PJG (1998e). The distribution of the GPS baseline in case of integer leastsquares ambiguity estimation. Artificial Satellites, 33(2): 65–75. Teunissen PJG (1999a). An optimality property of the integer least-squares estimator. Journal of Geodesy, 73: 587–593. Teunissen PJG (1999b). The probability distribution of the GPS baseline for a class of integer ambiguity estimators. Journal of Geodesy, 73: 275–284. Teunissen PJG (2000a). Adjustment theory; an introduction. Delft University Press, Delft. Teunissen PJG (2000b). ADOP based upperbounds for the bootstrapped and the leastsquares ambiguity success rates. Artificial Satellites, 35(4): 171–179. Teunissen PJG (2001a). Integer estimation in the presence of biases. Journal of Geodesy, 75: 399–407. Teunissen PJG (2001b). Statistical GNSS carrier phase ambiguity resolution: a review. Proc. of 2001 IEEE Workshop on Statistical Signal Processing, August 6-8, Singapore: 4–12. Teunissen PJG (2002). The parameter distributions of the integer GPS model. Journal of Geodesy, 76: 41–48. Teunissen PJG (2003a). A carrier phase ambiguity estimator with easy-to-evaluate failrate. Artificial Satellites, 38(3): 89–96. Teunissen PJG (2003b). An invariant upperbound for the GNSS bootstrapped ambiguity success rate. Journal of Global Positioning Systems, 2(1): 13–17. Teunissen PJG (2003c). GNSS Best Integer Equivariant Estimation. Accepted for publication in: Proc. of IUGG2003, session G.04, June 30 - July 11, Sapporo, Japan. Teunissen PJG (2003d). Integer aperture GNSS ambiguity resolution. Artificial Satellites, 38(3): 79–88. Teunissen PJG (2003e). Theory of integer aperture estimation with application to GNSS. MGP report, Delft University of Technology. Teunissen PJG (2003f). Theory of integer equivariant estimation with application to GNSS. Journal of Geodesy, 77: 402–410. 166 Bibliography
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The GNSS integer ambiguities: estim
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The GNSS integer ambiguities: estim
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Contents Preface v Summary vii Same
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4 Best Integer Equivariant estimati
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Preface It was in the beginning of
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• No attempt is made to fix the a
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Samenvatting (in Dutch) De GNSS geh
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gelegd door de keuze van de maximaa
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d, δ instrumental delay for code a
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Acronyms ADOP Ambiguity Dilution Of
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in practice, a user has to choose b
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GNSS observation model and quality
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Table 2.2: Signal and frequency pla
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2.2.2 Phase observations The phase
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the propagation delay does not depe
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2.2.9 The geometry-based observatio
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2.3.2 Single difference models If o
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and difficult to predict. Therefore
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The double difference observation v
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(appendix A.1): Qy = C sd pφ ⊗ D
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The quality of the solution can the
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is maximum. The degrees of freedom
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* â Figure 3.1: An ambiguity pull-
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2 1.5 1 0.5 0 −0.5 −1 −1.5
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estimator is given by: n Sz,B = x
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7 6 5 4 3 2 1 0 −1 −2 −3 −4
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Table 3.1: Overview of ambiguity re
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1 0.5 0 −2 −1 0 1 z 2 1 0 −1
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and has units of cycles. It was int
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chosen equal to half the number of
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Table 3.2: Two-dimensional example.
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The bias-affected success rate is a
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is close to one. This probability c
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2 0 −2 0.5 0 −0.5 2 0 −2 −4
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error in pdf error in pdf error in
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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 2.2
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acceptable. Moreover, the bounds wi
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Unfortunately, this relatively simp
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always larger than one. This shows
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where χ2 α(m−p, 0) is the criti
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Table 3.5: Overview of all test sta
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with the weight function wz(â) = 1
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IE IEU IU LU Figure 4.1: The set of
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4.2 Approximation of the BIE estima
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4.3 Comparison of the float, fixed,
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variane ratio 1.4 1.2 1 0.8 0.6 0.4
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ambiguity residual 0.5 0.4 0.3 0.2
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Table 4.1: Probabilities P1 = P (|
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Table 4.2: Probabilities Ps = P (ǎ
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Table 4.4: Probabilities that float
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probability probability 1 0.9 0.8 0
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Integer Aperture estimation 5 In se
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can be distinguished: â ∈ Ωa s
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and the hybrid distribution of ā i
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Figure 5.3: 2-D example for EIA est
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as follows: Ωz,R = ΩR ∩ Sz =
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3 2.5 2 1.5 1 0.5 0 −0.5 −1 −
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5.3.3 Difference test is an IA esti
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Figure 5.9: 2-D example for DTIA es
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Figure 5.11: 2-D example for PTIA e
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Figure 5.12: 2-D example for IAB es
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2-D example Figure 5.13 shows in bl
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µ 200 100 10 2 1 1 1.1 1.2 1.3 1.4
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5.6 Optimal Integer Aperture estima
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The optimization problem of (5.49)
Page 141 and 142: Table 5.1: Comparison of IA estimat
Page 143 and 144: µ 1.5 1.45 1.4 1.35 1.3 1.25 1.2 1
Page 145 and 146: In order to show that the fail rate
Page 147 and 148: success rate percentage identical 0
Page 149 and 150: probability probability 1 0.9 0.8 0
Page 151 and 152: 5.8.2 OIA estimation versus RTIA an
Page 153 and 154: µ µ µ 0.7 0.6 0.5 0.4 0.3 0.2 0.
Page 155 and 156: 0.6 0.4 0.2 0 −0.2 −0.4 −0.6
Page 157 and 158: three vc-matrices which are scaled
Page 159 and 160: Table 5.3: Comparison of IAB and IA
Page 161 and 162: success rate if fixed 1 0.95 0.9 0.
Page 163: Table 5.4: Overview of IA estimator
Page 166 and 167: IE IA I Figure 6.1: The set of rela
Page 168 and 169: convex region symmetric with respec
Page 171 and 172: Mathematics and statistics A A.1 Kr
Page 173 and 174: The expectation, E{x}, and the disp
Page 175 and 176: Choose the tolerance ε. Determine
Page 177 and 178: Simulation and examples B Throughou
Page 179 and 180: Theory of BIE estimation C In chapt
Page 181 and 182: The first term on the right-hand si
Page 183: can be derived: L = {2h(x) T Q
Page 186 and 187: 1. Choose fixed fail rate: Pf = β
Page 189 and 190: Bibliography Abidin HA (1993). Comp
Page 191: Jung J, Enge P, Pervan B (2000). Op
Page 195 and 196: Index adjacent, 33 ADOP, 42 alterna
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