Statistical Estimation and Tracking of Refractivity from Radar Clutter

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$Refractivty estimation from radar clutter - the Marine Physical ...$

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Figure 3.6: Convergence in GA: Effect of GA sample size on 1-D marginal posterior densities for a 40k Gibbs sample size. Distributions calculated using (a) exhaustive search and the hybrid method with (b) 1k, (c) 5k, and (d) 15k GA samples. . . . . . . . . . . 81 Figure 3.7: Convergence in GS: Effect of GS sample size on 1-D marginal posterior densities for a 15k GA sample size. Distributions calculated using (a) exhaustive search and the hybrid method with (b) 1k, (c) 5k, and (d) 20k Gibbs samples. . . . . . . . . . . . . 82 Figure 3.8: Convergence of the hybrid method. D for each parameter as a function of (a) GA sample size for a 40k Gibbs sample size and (b) Gibbs sample size for a 15k GA sample size . . . . . . . 83 Figure 3.9: An example of range-dependent sixteen parameter M-profile with four parameters per 20 km. Vertical profile at any given range is calculated by linear interpolation of both the slopes and the layer thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . 84 Figure 3.10: Results for the Wallops data. (a) estimated and helicoptermeasured profiles at various ranges and (b) SPANDAR clutter together with the clutter that one would obtain from the estimated range-dependent and independent environments. . . . . . 85 Figure 3.11: Marginal and conditional distributions. (a)1-D (diagonal) and 2-D (upper diagonal) posterior probability distributions in terms of percent HPD, for the range-dependent SPANDAR data inversion. (b) Error function for conditional planes. . . . . . . . 88 Figure 3.12: Posterior densities for propagation factor F at three different ranges. Color plots show the PPD of F for height values between 0 m and 200 m in terms of percent HPD, with the MAP solution (dashed white). . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Figure 3.13: Posterior probability densities for propagation factor F at (a) 20 and (b) 100 m altitudes. Color plots show the PPD of F for ranges between 0–90 km in terms of percent HPD, with the dashed white line showing the MAP solution. . . . . . . . . . . 92 Figure 4.1: Ten 2-D M-profiles measured by JHU helicopter, Wallops’98 experiment (gray) and best trilinear profile fit for each measurement (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Figure 4.2: Case study I. (a) Regional map and the location of the station (×), (b) average spring M-profile, (c) 100 Monte Carlo trajectories, and (d) RMS errors of the EKF, UKF, and 200-particle PF along with the square root of the posterior CRLB. . . . . . 115 Figure 4.3: Efficiency of the PF as a function of the number of particles. 117 Figure 4.4: Case Study II: Temporal evolution of the range-independent duct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Figure 4.5: Evolution of the highly nonlinear relative radar clutter y k (dB) computed for the true environment without w k . . . . . . . 118 x
Figure 4.6: Case Study II: Temporal tracking of the range-independent SBD. c 1 and c 2 are in M-units/m and h 1 and h 2 are in meters. True trajectories (dashed) and filter estimates (solid) for the EKF, UKF and PF-200. . . . . . . . . . . . . . . . . . . . . . . 119 Figure 4.7: Case Study III. (a) EDH statistics and (b) air-sea temperature difference, (c) spatio-temporal evolution of the EDH, (d) 2-D M-profiles, and (e) the evolution of the EDH for the selected range grid that is used to construct the state vector x k . . . . . . 123 xi
Page 1 and 2: UNIVERSITY OF CALIFORNIA, SAN DIEGO
Page 3 and 4: The dissertation of Caglar Yardim i
Page 5 and 6: TABLE OF CONTENTS Signature Page .
Page 7 and 8: 4.5 Discussion . . . . . . . . . .
Page 9: Figure 2.10: Marginal posterior pro
Page 13 and 14: ACKNOWLEDGMENTS I would like to gen
Page 15 and 16: VITA 1998 B.S. in Electrical Engine
Page 17 and 18: Major Field: Electrical Engineering
Page 19 and 20: The first part of this thesis discu
Page 21 and 22: 2 models. 2. Electromagnetic Theory
Page 23 and 24: 4 in nature. On the other hand if t
Page 25 and 26: 6 over the coastal regions and the
Page 27 and 28: 8 is no more bounded below by the s
Page 29 and 30: 10 Fig. 1.3 (b) shows what happens
Page 31 and 32: 12 Doppler spread radars [5] are an
Page 33 and 34: 14 1.3.1 Tropospheric Propagation U
Page 35 and 36: 16 Now the wave equation can readil
Page 37 and 38: 18 solution for U(r, p) as −p 2
Page 39 and 40: 20 where C accounts for all the con
Page 41 and 42: 22 Figure 1.5: Sea surface grazing
Page 43 and 44: 24 atmospheric index of refraction
Page 45 and 46: 26 implementation of the PF. Both K
Page 47 and 48: 28 [12] Amalia E. Barrios. Paraboli
Page 49 and 50: 2 Estimation of Radio Refractivity
Page 51 and 52: 32 requiring any additional measure
Page 53 and 54: 34 sity (PPD), which can be accompl
Page 55 and 56: 36 Posterior density of any specifi
Page 57 and 58: 38 set up the MCMC such that the de
Page 59 and 60: 40 2.2.4 Monte Carlo Integration Mo
Page 61 and 62:
42 parameter axes, it is hard to sa
Page 63 and 64:
44 2.3.4 Post-Processing After the
Page 65 and 66:
46 Figure 2.5: Initial sampling pha
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48 0.04 c 1 −2.6 −2.4 −2.2 0.
Page 69 and 70:
50 VA Wallops Is. SPANDAR Helicopte
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52 0.05 c 1 0 −1 −0.5 0 M−uni
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54 (a) 200 −100 (d) 200 150 100 5
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56 (a) 0.2 (b) 0.2 0.15 0.15 PPD(F)
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58 d m f(·) f(m) φ(m) n N R N N e
Page 79 and 80:
60 Bibliography [1] S. Vasudevan an
Page 81 and 82:
[25] Julius Goldhirsh and Daniel Do
Page 83 and 84:
64 Hastings (M-H) and Gibbs samplin
Page 85 and 86:
66 dimensional integrals of the joi
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68 where C d is the data error cova
Page 89 and 90:
70 By introducing a weight function
Page 91 and 92:
72 entire search space and there is
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74 3. Gibbs Resampling: Run a fast
Page 95 and 96:
76 Figure 3.2: Voronoi cells and a
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78 (a) 5 c 1 5 5 5 h 2 (b) 0 0.1 0.
Page 99 and 100:
80 density. However, it is sampling
Page 101 and 102:
82 (a) 5 c 1 5 5 5 h 2 (b) 0 0.1 0.
Page 103 and 104:
84 Figure 3.9: An example of range-
Page 105 and 106:
86 full PPD is 16-D, only 1-D (diag
Page 107 and 108:
88 Figure 3.11: Marginal and condit
Page 109 and 110:
90 Table 3.3: Wallops’98 Experime
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92 Propagation Factor, F (dB) Propa
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94 [11] L. Ted Rogers, Michael Jabl
Page 115 and 116:
4 Tracking Refractivity From Clutte
Page 117 and 118:
98 structure. These techniques can
Page 119 and 120:
100 the filter performance still he
Page 121 and 122:
102 ing autocorrelation function. T
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104 in range using the following re
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106 4.3.2 Unscented Kalman Filter T
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108 4.3.3 Particle Filter The last
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110 Let J k be the inverse of the C
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112 Table 4.1: Case Study I: Compar
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Table 4.2: Performance Comparison f
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116 performance. Therefore, it can
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118 error larger than 5 m for any 5
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120 Table 4.3: Performance Comparis
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122 Table 4.4: Case Study III: Coas
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124 Since the layer is thin it has
Page 145 and 146:
126 Bibliography [1] J. R. Rowland
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128 [23] R. A. Paulus. An overview
Page 149 and 150:
5 Conclusions and Future Work 5.1 C
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132 • A hybrid GA-MCMC method bas
Page 153 and 154:
134 Kalman filters performed remark
Page 155:
136 mance predictions of the EKF, U
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Statistical Estimation and Tracking of Refractivity from Radar Clutter

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