Statistical Estimation and Tracking of Refractivity from Radar Clutter

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23 alarm rate. Environmental domain Data domain d m Usage domain Utility u Figure 1.6: An observation d is mapped into a distribution of environmental parameters m that potentially could have generated it. These environmental parameters are then mapped into the usage domain u. The list of techniques used in this work are given as below. Each of these techniques is summarized in their prospective chapters. • Genetic Algorithms (GA) • Simulated Annealing (SA) • Metropolis-Hastings (MCMC) Sampler • Gibbs (MCMC) Sampler • Hybrid GA-MCMC Sampler • Extended Kalman Filter (EKF) • Unscented Kalman Filter (UKF) • Sequential Importance Resampling Particle Filter (SIR-PF) 1.5 Scope of This Dissertation The major contents of this dissertation consist of three chapters, Chapters 2 to 5 1 . The first two of these chapters deals with the statistical estimation of the 1 Each chapter is essentially a full or partial reprint of papers that are published, accepted, or submitted to a professional journal. Therefore, each has been written in a paper format and is self-contained.
24 atmospheric index of refraction while Chapter 5 covers the spatial and temporal tracking of it. Chapter 2 is devoted to the analysis of the RFC inversion problem using different Markov chain Monte Carlo samplers (MCMC) [22]. A typical rangeindependent tri-linear surface-based electromagnetic duct is estimated statistically using Metropolis-Hastings [23] and Gibbs [24] samplers. The main purpose is estimating statistically the uncertainties in the environmental parameters and projecting these into the posterior probability densities of transmission loss and propagation factor using Monte Carlo integration that can be used to predict and in some cases correct the radar performance operating in such an environment. The results are checked with exhaustive search and compared with previous studies conducted using genetic algorithms [17]. The methods are then successfully tested on data collected during the Wallops Island 1998 experiment conducted by the Naval Surface Warfare Center, Dahlgren Division that included both range-dependent environmental refractivity measurements using the helicopter provided by the Applied Physics Laboratory, John Hopkins University and radar clutter maps obtained during the operation of the Space Range Radar (SPANDAR). The results showed that these methods can accurately compute the required Monte Carlo integrations but needed high number of forward model runs which are composed of propagating the electromagnetic signal in these complex environments using the split-step FFT PE method and hence are not suitable for a real or near-real time statistical RFC estimator. Moreover, inclusion of range-dependence results in an increase in the number of environmental parameters to be estimated and an increased dimension of the parameter state-space, making these algorithm even less suitable for realtime applications. This resulted in a search for techniques that would necessitate fewer forward model runs with a minimal degradation in the MCMC performance. This problem is addressed in Chapter 3. A hybrid genetic algorithms (GA) – Markov chain Monte Carlo method [25] based on the nearest neighborhood algorithm proposed in [26,27] is implemented. This method uses a Voronoi
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 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: 22 Figure 1.5: Sea surface grazing
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
Page 83 and 84: 64 Hastings (M-H) and Gibbs samplin
Page 85 and 86: 66 dimensional integrals of the joi
Page 87 and 88: 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
Page 97 and 98:
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
Page 115 and 116:
4 Tracking Refractivity From Clutte
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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
Page 135 and 136:
116 performance. Therefore, it can
Page 137 and 138:
118 error larger than 5 m for any 5
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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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