The GNSS integer ambiguities: estimation and validation

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Acronyms ADOP Ambiguity Dilution Of Precision B integer Bootstrapping BIE Best Integer Equivariant CIR Cascade Integer Resolutoin DIA Detection-Identification-Adaptation DD Double Difference DGNSS Differential GNSS DGPS Differential GPS EIA Ellipsoidal Integer Aperture GLONASS GLObal NAvigation Satellite System (Russian) GNSS Global Navigation Satellite System GPS Global Positioning System IA Integer Aperture IAB Integer Aperture Bootstrapping IALS Integer Aperture Least-Squares IE Integer Equivariant ILS Integer Least-Squares ITCAR Integrated TCAR LAMBDA Least-squares AMBiguity Decorrelation Adjustment LOM Local Overall Model (test) LOS Line-Of-Sight LS Least-Squares MDB Minimal Detectable Bias MDE Minimal Detectable Effect OIA Optimal Integer Aperture OTF On-The-Fly PDF Probability Density Function PIA Penalized Integer Aperture PMF Probability Mass Function R integer Rounding RTK Real-Time Kinematic SD Single Difference TCAR Three Carrier Ambiguity Resolution TEC Total Electron Content ZTD Zenith Tropospheric Delay xix
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 27 and 28: Introduction 1 1.1 Background In th
Page 29: The contribution of this thesis is
Page 32 and 33: Table 2.1: Signal and frequency pla
Page 34 and 35: of reception diminished with the si
Page 36 and 37: 2.2.3 Signal travel time In the pre
Page 38 and 39: 2.2.6 Multipath Ideally, a GNSS sig
Page 40 and 41: Table 2.3: Availability and accurac
Page 42 and 43: with ep a p-vector with ones, Ip an
Page 44 and 45: The single difference models can no
Page 46 and 47: The single difference approach can
Page 48 and 49: 2.4.3 Cross-correlation and time co
Page 50 and 51: So, λ0 = λ(αq, γ0, q). From thi
Page 53 and 54: Integer ambiguity resolution 3 The
Page 55 and 56: Figure 3.2: Left: Pull-in regions t
Page 57 and 58: 2 1 0 −1 −2 −2 −1 0 1 2 Fig
Page 59 and 60: 2 1 0 −1 −2 −2 −1 0 1 2 Fig
Page 61 and 62: matrix D. From equation (3.21) the
Page 63 and 64: 3.2.1 Parameter distributions of th
Page 65 and 66: have to be used. The most important
Page 67 and 68: Then Ua = {â ∈ R n | p ∩ i=1 |
Page 69 and 70: success rate 1 0.9 0.8 0.7 0.6 0.5
Page 71 and 72: on bounding the integration region
Page 73 and 74: for any R, it follows that the PDF
Page 75 and 76:
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 σ=0
Page 77 and 78:
2 1 0 −1 −2 −2 −1 0 1 2 0.4
Page 79 and 80:
Table 3.4: Order of the mean and ma
Page 81 and 82:
3.4.2 Baseline probabilities The qu
Page 83 and 84:
probability probability 1 0.9 0.8 0
Page 85 and 86:
Since H3 ⊂ H1 ⊂ H2, starting po
Page 87 and 88:
where F (n, m − n − p, λi) den
Page 89 and 90:
The test is then defined by the con
Page 91 and 92:
validation criteria. The fundamenta
Page 93 and 94:
Best Integer Equivariant estimation
Page 95 and 96:
where y ∈ R m with mean E{y} = Aa
Page 97 and 98:
difference between the BIE estimato
Page 99 and 100:
elative frequency relative frequenc
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estimator 1.5 1 0.5 0 −0.5 −1
Page 103 and 104:
probability 1 0.8 0.6 0.4 0.2 0 200
Page 105 and 106:
0.6 0.4 0.2 0 −0.2 −0.4 −0.6
Page 107 and 108:
probability 1 0.9 0.8 0.7 0.6 0.5 0
Page 109 and 110:
Note that since ˜ɛ 2 Qˆz ≤ ˇ
Page 111:
squared norm of ambiguity residuals
Page 114 and 115:
5.1 Integer Aperture estimation The
Page 116 and 117:
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05
Page 118 and 119:
1.5 1 0.5 0 −0.5 −1 −1.5 −1
Page 120 and 121:
2-D example Figure 5.3 shows in bla
Page 122 and 123:
1 0.5 0 −0.5 −1 −1 −0.5 0 0
Page 124 and 125:
Figure 5.7: 2-D example for F -RTIA
Page 126 and 127:
1 0.5 0 −0.5 −1 −1 −0.5 0 0
Page 128 and 129:
1 0.5 0 −0.5 −1 −1 −0.5 0 0
Page 130 and 131:
success rate and fail rate. From eq
Page 132 and 133:
Figure 5.13: 2-D example for IALS e
Page 134 and 135:
Therefore, the average penalty also
Page 136 and 137:
0.5 0 −0.5 0.5 0 −0.5 0.5 0 −
Page 138 and 139:
Clearly, the region ˆ Ω in (5.51
Page 140 and 141:
Figure 5.16: 2-D example for OIA es
Page 142 and 143:
0.6 0.4 0.2 0 −0.2 −0.4 −0.6
Page 144 and 145:
oundary of the aperture pull-in reg
Page 146 and 147:
Table 5.2: Comparison of IA estimat
Page 148 and 149:
success rate percentage identical 1
Page 150 and 151:
probability probability 1 0.9 0.8 0
Page 152 and 153:
This means that the higher the prec
Page 154 and 155:
in order to guarantee a low fail ra
Page 156 and 157:
µ success rate 1.4 1.35 1.3 1.25 1
Page 158 and 159:
µ success rate / undecided rate 0.
Page 160 and 161:
P fix 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
Page 162 and 163:
implies that the success rate incre
Page 165 and 166:
Conclusions and recommendations 6 6
Page 167 and 168:
• The discrimination tests - rati
Page 169:
6.4 Bias robustness In the precedin
Page 172 and 173:
Let x be normally distributed with
Page 174 and 175:
The following notation is used: x
Page 176 and 177:
Determine the zero-crossing of the
Page 178 and 179:
Table B.1: Time, location, number o
Page 180 and 181:
So that: 0 = E{g(â)} = g(x)fâ(x
Page 182 and 183:
C.4 Best integer equivariant unbias
Page 185 and 186:
Implementation aspects of IALS esti
Page 187:
Curriculum vitae E Sandra Verhagen
Page 190 and 191:
Euler HJ, Goad C (1991). On optimal
Page 192 and 193:
Teunissen PJG (1995). The least-squ
Page 194 and 195:
Verhagen S, Teunissen PJG (2004c).
Page 196:
probability density function, 37 pr
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