The GNSS integer ambiguities: estimation and validation

More documents

Recommendations

Info

1. Choose fixed fail rate: Pf = β 2. Collect observations and apply least-squares adjustment: â, Qâ; 3. Apply integer least-squares estimation: ǎ, ˇɛ, ǎ2; 4. Choose µ ′ as described above; 5. Generate N samples of float ambiguities ˆxi ∼ N(0, Qâ); 6. For each sample determine the ILS estimate ˇxi 1 and ui = arg min z∈Zn µ (ˆxi − ˇxi) − z2 Qˆx ; 7. Count number of samples Nf for which: ui = 0 and ˇxi = 0; 8. Compute fail rate with µ ′ as critical value: Pf (µ ′ ) = Nf N ; 9. If Pf (µ ′ ) ≤ β: ā = ǎ, otherwise ā = â; Note that in step 6 ILS estimation has to be carried out twice for each sample. This might be very time-consuming if the number of samples, N, is large. 160 Implementation aspects of IALS estimation
Curriculum vitae E Sandra Verhagen (1976) was born in Leidschendam, The Netherlands. 1988 - 1994 Alfrink College, Zoetermeer 1994 - 2000 Geodetic Engineering, Delft University of Technology Thesis: Time variations in the gravity field - The effect of the atmosphere 2000 - 2004 PhD researcher, Mathematical Geodesy and Positioning 2003 ESA project Analysis of ambiguity resolution algorithms and quality control parameters for Global Navigation Satellite Systems 161
Page 1:
The GNSS integer ambiguities: estim
Page 4 and 5:
The GNSS integer ambiguities: estim
Page 7 and 8:
Contents Preface v Summary vii Same
Page 9 and 10:
4 Best Integer Equivariant estimati
Page 11:
Preface It was in the beginning of
Page 14 and 15:
• No attempt is made to fix the a
Page 17 and 18:
Samenvatting (in Dutch) De GNSS geh
Page 19:
gelegd door de keuze van de maximaa
Page 22 and 23:
d, δ instrumental delay for code a
Page 25:
Acronyms ADOP Ambiguity Dilution Of
Page 28 and 29:
in practice, a user has to choose b
Page 31 and 32:
GNSS observation model and quality
Page 33 and 34:
Table 2.2: Signal and frequency pla
Page 35 and 36:
2.2.2 Phase observations The phase
Page 37 and 38:
the propagation delay does not depe
Page 39 and 40:
2.2.9 The geometry-based observatio
Page 41 and 42:
2.3.2 Single difference models If o
Page 43 and 44:
and difficult to predict. Therefore
Page 45 and 46:
The double difference observation v
Page 47 and 48:
(appendix A.1): Qy = C sd pφ ⊗ D
Page 49 and 50:
The quality of the solution can the
Page 51:
is maximum. The degrees of freedom
Page 54 and 55:
* â Figure 3.1: An ambiguity pull-
Page 56 and 57:
2 1.5 1 0.5 0 −0.5 −1 −1.5
Page 58 and 59:
estimator is given by: n Sz,B = x
Page 60 and 61:
7 6 5 4 3 2 1 0 −1 −2 −3 −4
Page 62 and 63:
Table 3.1: Overview of ambiguity re
Page 64 and 65:
1 0.5 0 −2 −1 0 1 z 2 1 0 −1
Page 66 and 67:
and has units of cycles. It was int
Page 68 and 69:
chosen equal to half the number of
Page 70 and 71:
Table 3.2: Two-dimensional example.
Page 72 and 73:
The bias-affected success rate is a
Page 74 and 75:
is close to one. This probability c
Page 76 and 77:
2 0 −2 0.5 0 −0.5 2 0 −2 −4
Page 78 and 79:
error in pdf error in pdf error in
Page 80 and 81:
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 2.2
Page 82 and 83:
acceptable. Moreover, the bounds wi
Page 84 and 85:
Unfortunately, this relatively simp
Page 86 and 87:
always larger than one. This shows
Page 88 and 89:
where χ2 α(m−p, 0) is the criti
Page 90 and 91:
Table 3.5: Overview of all test sta
Page 92 and 93:
with the weight function wz(â) = 1
Page 94 and 95:
IE IEU IU LU Figure 4.1: The set of
Page 96 and 97:
4.2 Approximation of the BIE estima
Page 98 and 99:
4.3 Comparison of the float, fixed,
Page 100 and 101:
variane ratio 1.4 1.2 1 0.8 0.6 0.4
Page 102 and 103:
ambiguity residual 0.5 0.4 0.3 0.2
Page 104 and 105:
Table 4.1: Probabilities P1 = P (|
Page 106 and 107:
Table 4.2: Probabilities Ps = P (ǎ
Page 108 and 109:
Table 4.4: Probabilities that float
Page 110 and 111:
probability probability 1 0.9 0.8 0
Page 113 and 114:
Integer Aperture estimation 5 In se
Page 115 and 116:
can be distinguished: â ∈ Ωa s
Page 117 and 118:
and the hybrid distribution of ā i
Page 119 and 120:
Figure 5.3: 2-D example for EIA est
Page 121 and 122:
as follows: Ωz,R = ΩR ∩ Sz =
Page 123 and 124:
3 2.5 2 1.5 1 0.5 0 −0.5 −1 −
Page 125 and 126:
5.3.3 Difference test is an IA esti
Page 127 and 128:
Figure 5.9: 2-D example for DTIA es
Page 129 and 130:
Figure 5.11: 2-D example for PTIA e
Page 131 and 132:
Figure 5.12: 2-D example for IAB es
Page 133 and 134:
2-D example Figure 5.13 shows in bl
Page 135 and 136: µ 200 100 10 2 1 1 1.1 1.2 1.3 1.4
Page 137 and 138: 5.6 Optimal Integer Aperture estima
Page 139 and 140: 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 189 and 190: Bibliography Abidin HA (1993). Comp
Page 191 and 192: Jung J, Enge P, Pervan B (2000). Op
Page 193 and 194: Teunissen PJG (2003g). Towards a un
Page 195 and 196: Index adjacent, 33 ADOP, 42 alterna
show all

The GNSS integer ambiguities: estimation and validation

Create successful ePaper yourself

Delete template?

Save as template?