Statistical Estimation and Tracking of Refractivity from Radar Clutter

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ABSTRACT OF THE DISSERTATION Statistical Estimation and Tracking of Refractivity from Radar Clutter by Caglar Yardim Doctor of Philosophy in Electrical Engineering (Applied Ocean Sciences) University of California, San Diego, 2007 William S. Hodgkiss, Chair Kenneth Kreutz-Delgado, Co-Chair In many maritime regions of the world, such as the Mediterranean, Persian Gulf, East China Sea, and the Californian Coast, atmospheric ducts are common occurrences. They result in various anomalies such as significant variations in the maximum operational radar range, creation of regions where the radar is practically blind (radar holes) and increased sea clutter. Therefore, it is important to predict the real-time 3-D environment in which the radar is operating so that the radar operator will at least know the true system limitations and in some cases even compensate for them. This dissertation addresses the estimation and tracking of the lower atmospheric radio refractivity under non-standard propagation conditions frequently encountered in low altitude maritime radar applications. This is done by statistically estimating the duct strength (range and height-dependent atmospheric index of refraction) from the sea-surface reflected radar clutter. Therefore, such methods are called Refractivity From Clutter (RFC) techniques. These environmental statistics can then be used to predict the radar performance. The electromagnetic propagation in these complex environments is simulated using a split-step fast Fourier transform (FFT) based parabolic equation (PE) approximation to the wave equation. xviii
The first part of this thesis discusses various algorithms such as genetic algorithms (GA), Markov chain Monte Carlo samplers (MCMC) and the hybrid GA-MCMC samplers that are used to estimate atmospheric radio refractivity for a given azimuth direction and time. The results show that radar clutter can be a rich source of information about the environment and the techniques mentioned above are used successfully as near real-time estimators for the data collected during the Wallops’98 experiment conducted by the Naval Surface Warfare Center. The second part of this dissertation focuses on both spatial and temporal tracking of the 3-D environment. Techniques such as the extended (EKF) and unscented (UKF) Kalman filters, and particle filters (PF) are used for tracking the spatial and temporal evolution of the lower atmosphere. Even though the tracking performance of the Kalman filters was limited for certain duct types such as the surface-based ducts due to the high non-linearity of the split-step FFT PE, they performed well for other environments such as evaporation ducts. On the other hand, particle filters proved to be very promising in tracking a wide variety of scenarios including even abruptly changing environments. xix
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: Major Field: Electrical Engineering
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
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
Page 111 and 112:
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
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
Page 133 and 134:
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
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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