The GNSS integer ambiguities: estimation and validation

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The GNSS integer ambiguities: estimation and validation Sandra Verhagen NCG Nederlandse Commissie voor Geodesie Netherlands Geodetic Commission Delft, January 2005
Page 1: The GNSS integer ambiguities: estim
Page 5: Precision is a quest on which trave
Page 8 and 9: 2.3 GNSS functional model . . . . .
Page 10 and 11: 5.10 Summary . . . . . . . . . . .
Page 13 and 14: Summary The GNSS integer ambiguitie
Page 15: Finally, it is shown that the popul
Page 18 and 19: • Validatie van de geheeltallige
Page 21 and 22: Notation and symbols Mathematical n
Page 23: Parameter distributions fˆx(x) pro
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
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Figure 3.2: Left: Pull-in regions t
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2 1 0 −1 −2 −2 −1 0 1 2 Fig
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2 1 0 −1 −2 −2 −1 0 1 2 Fig
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matrix D. From equation (3.21) the
Page 63 and 64:
3.2.1 Parameter distributions of th
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have to be used. The most important
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Then Ua = {â ∈ R n | p ∩ i=1 |
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success rate 1 0.9 0.8 0.7 0.6 0.5
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on bounding the integration region
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for any R, it follows that the PDF
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5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 σ=0
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2 1 0 −1 −2 −2 −1 0 1 2 0.4
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Table 3.4: Order of the mean and ma
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3.4.2 Baseline probabilities The qu
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probability probability 1 0.9 0.8 0
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Since H3 ⊂ H1 ⊂ H2, starting po
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where F (n, m − n − p, λi) den
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The test is then defined by the con
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validation criteria. The fundamenta
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Best Integer Equivariant estimation
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where y ∈ R m with mean E{y} = Aa
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difference between the BIE estimato
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elative frequency relative frequenc
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estimator 1.5 1 0.5 0 −0.5 −1
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probability 1 0.8 0.6 0.4 0.2 0 200
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0.6 0.4 0.2 0 −0.2 −0.4 −0.6
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probability 1 0.9 0.8 0.7 0.6 0.5 0
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Note that since ˜ɛ 2 Qˆz ≤ ˇ
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squared norm of ambiguity residuals
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5.1 Integer Aperture estimation The
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0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05
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1.5 1 0.5 0 −0.5 −1 −1.5 −1
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2-D example Figure 5.3 shows in bla
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1 0.5 0 −0.5 −1 −1 −0.5 0 0
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Figure 5.7: 2-D example for F -RTIA
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1 0.5 0 −0.5 −1 −1 −0.5 0 0
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1 0.5 0 −0.5 −1 −1 −0.5 0 0
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success rate and fail rate. From eq
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Figure 5.13: 2-D example for IALS e
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Therefore, the average penalty also
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0.5 0 −0.5 0.5 0 −0.5 0.5 0 −
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Clearly, the region ˆ Ω in (5.51
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Figure 5.16: 2-D example for OIA es
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0.6 0.4 0.2 0 −0.2 −0.4 −0.6
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oundary of the aperture pull-in reg
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Table 5.2: Comparison of IA estimat
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success rate percentage identical 1
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probability probability 1 0.9 0.8 0
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This means that the higher the prec
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in order to guarantee a low fail ra
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µ success rate 1.4 1.35 1.3 1.25 1
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µ success rate / undecided rate 0.
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P fix 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
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implies that the success rate incre
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Conclusions and recommendations 6 6
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• The discrimination tests - rati
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6.4 Bias robustness In the precedin
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Let x be normally distributed with
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The following notation is used: x
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Determine the zero-crossing of the
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Table B.1: Time, location, number o
Page 180 and 181:
So that: 0 = E{g(â)} = g(x)fâ(x
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C.4 Best integer equivariant unbias
Page 185 and 186:
Implementation aspects of IALS esti
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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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