Statistical Estimation and Tracking of Refractivity from Radar Clutter

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

$Statistical Estimation of Refractivity from Radar Sea Clutter$

$Real time refractivity from clutter using a best fit ... - CiteSeerX$

2.3.3 Final Sampling Phase and Convergence . . . . . . . . . . . . 42 2.3.4 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4.1 Algorithm Validation . . . . . . . . . . . . . . . . . . . . . . 44 2.4.2 Wallops Island Experiment . . . . . . . . . . . . . . . . . . . 48 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.6 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 Statistical Maritime Radar Duct Estimation Using a Hybrid Genetic Algorithms – Markov Chain Monte Carlo Method . . . . . . . . . . . . 63 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3 The Hybrid GA-MCMC Method . . . . . . . . . . . . . . . . . . . 69 3.3.1 Monte Carlo Integration and Genetic Algorithms . . . . . . . 69 3.3.2 Voronoi Decomposition . . . . . . . . . . . . . . . . . . . . . 70 3.3.3 MCMC (Gibbs) Resampling . . . . . . . . . . . . . . . . . . . 72 3.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4.2 Wallops’98 Data . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.6 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4 Tracking Refractivity From Clutter . . . . . . . . . . . . . . . . . . . . 96 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.2.1 Creation of the 2-D Modified Refractivity Profile from State Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.2.2 State Equation – Environmental Model . . . . . . . . . . . . 101 4.2.3 Measurement Equation – Propagation Model . . . . . . . . . 103 4.3 Tracking Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.3.1 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . 105 4.3.2 Unscented Kalman Filter . . . . . . . . . . . . . . . . . . . . 106 4.3.3 Particle Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3.4 Posterior Cramér-Rao Lower Bound . . . . . . . . . . . . . . 109 4.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.1 Case Study I: Temporal Tracking of a Range-Independent Surface-Based Duct . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.2 Case Study II: Divergence in Surface-Based Duct Tracking . . 116 4.4.3 Case Study III: Range-Dependent Evaporation Duct Tracking in Coastal Regions . . . . . . . . . . . . . . . . . . . . . . . . 119 vi
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.7 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . 130 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.1.1 Statistical Estimation of Refractivity . . . . . . . . . . . . . . 130 5.1.2 Refractivity Tracking . . . . . . . . . . . . . . . . . . . . . . 132 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 vii
Page 1 and 2: UNIVERSITY OF CALIFORNIA, SAN DIEGO
Page 3 and 4: The dissertation of Caglar Yardim i
Page 5: TABLE OF CONTENTS Signature Page .
Page 9 and 10: Figure 2.10: Marginal posterior pro
Page 11 and 12: Figure 4.6: Case Study II: Temporal
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
Page 67 and 68:
48 0.04 c 1 −2.6 −2.4 −2.2 0.
Page 69 and 70:
50 VA Wallops Is. SPANDAR Helicopte
Page 71 and 72:
52 0.05 c 1 0 −1 −0.5 0 M−uni
Page 73 and 74:
54 (a) 200 −100 (d) 200 150 100 5
Page 75 and 76:
56 (a) 0.2 (b) 0.2 0.15 0.15 PPD(F)
Page 77 and 78:
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
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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
Page 93 and 94:
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
Page 113 and 114:
94 [11] L. Ted Rogers, Michael Jabl
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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
Page 123 and 124:
104 in range using the following re
Page 125 and 126:
106 4.3.2 Unscented Kalman Filter T
Page 127 and 128:
108 4.3.3 Particle Filter The last
Page 129 and 130:
110 Let J k be the inverse of the C
Page 131 and 132:
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
Page 139 and 140:
120 Table 4.3: Performance Comparis
Page 141 and 142:
122 Table 4.4: Case Study III: Coas
Page 143 and 144:
124 Since the layer is thin it has
Page 145 and 146:
126 Bibliography [1] J. R. Rowland
Page 147 and 148:
128 [23] R. A. Paulus. An overview
Page 149 and 150:
5 Conclusions and Future Work 5.1 C
Page 151 and 152:
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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