Sep 8, 2003 - Markov modeling (HMM) techniques to achieve superior HRR-ATR performance. ...... iterative procedure called the Baum-Welch algorithm is used to choose ...... [48] Bottcher, C. and Strayer, M.R. (1993), âClassical scattering ...
IMPROVED TARGET RECOGNITION AND TARGET DETECTION ALGORITHMS USING HRR PROFILES AND SAR IMAGES
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering
By
ANINDYA SANKAR PAUL B.E., Manipal Institute of Technology, India, 2001
2003 Wright State University
Wright State University School of Graduate Studies September 8, 2003 I HEREBY RECOMMEND THAT THE THESIS PRESENTED UNDER MY SUPERVISION BY Anindya Sankar Paul ENTITLED Improved Target Recognition and Target Detection Algorithms using HRR profiles and SAR images BE ACCEPTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master Of Science in Electrical Engineering. ______________________ Arnab K. Shaw, Ph.D. Thesis Director ______________________ Fred Garber, Ph.D. Department Chair Committee on Final Examination ___________________________ Arnab K. Shaw, Ph.D. ___________________________ Atindra K. Mitra, Ph.D. ___________________________ Fred Garber, Ph.D. ___________________________ Kefu Xue, Ph.D. ___________________________ Joseph F. Thomas, Jr., Ph.D. Dean, School of Graduate Studies
ABSTRACT Paul Anindya S. M.S.Eg., Department of Electrical Engineering, Wright State University, 2003: Improved Target Recognition and Target Detection Algorithms using HRR profiles and SAR images.
In this thesis, a new algorithm to improve automatic target recognition techniques on High Range Resolution (HRR) Profiles is presented and also a number of ways are investigated for target detection using Synthetic Aperture Radar (SAR) images. A new 1-D hybrid Automatic Target Recognition (ATR) algorithm is developed for sequential High Range Resolution (HRR) radar signatures. The proposed hybrid algorithm combines Eigen-Template based Matched Filtering (ETMF) and Hidden Markov modeling (HMM) techniques to achieve superior HRR-ATR performance. In the proposed hybrid approach, each HRR test profile is first scored by ETMF that is then followed by independent HMM scoring. The first ETMF scoring step produces a limited number of “most likely” models that are target and aspect dependent. These reduced numbers of models are then used for improved HMM scoring in the second step. Finally, the individual scores of ETMF and HMM are combined using Maximal Ratio Combining to render a classification decision. Classification results are presented for the MSTAR data set via ROC curves. An ultra-wideband (UWB) synthetic aperture radar (SAR) simulation technique that employs physical and statistical models is developed and presented. This joint
iii
physics/statistics based technique generates images that have many of the “blob-like” and “spiky” clutter characteristics of UWB radar data in forested regions while avoiding the intensive computations required for the implementation of low-frequency numerical electromagnetic simulation techniques. Comparative results from three SVD-based subspace filtering approaches on target detection algorithms are reported.
These
approaches are denoted as “Energy-Normalized SVD”, “Condition-Statistics SVD”, and “Terrain-Filtered SVD”. Approaches towards developing “self-training” algorithms for UWB radar target detection are investigated using the results of this simulation process.
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CONTENTS
1: Introduction
1
1.1 ATR/Target Detection review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1 A review of ATR/Target detection . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2 Moving Target Indicator (MTI) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.3 Synthetic Aperture Radar (SAR) . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.1.4 High Range Resolution Radar (HRR) . . . . . . . . . . . . . . . . . . . . . . .
6
1.2 Background and previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.3 Background on Automatic Target Recognition using HRR profiles . . . . . .
11
1.4 Background on Target Detection on SAR images . . . . . . . . . . . . . . . . . . . .
15
1.5 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2: Robust HRR Radar Target Identification by Hybridization of HMM and
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Eigen Template based Matched Filtering 2.1 ETMF Approach of training and classification . . . . . . . . . . . . . . . . . . . . . .
19
2.1.1 HRR Data Generation and Preprocessing . . . . . . . . . . . . . . . . . . . . . .
20
2.1.2: Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
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2.1.3: Alignment of HRR Profiles in Range . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.1.4: Eigen-analysis of HRR data for training . . . . . . . . . . . . . . . . . . . . . .
22
2.1.5: Unknown Target Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.1.6: Modified Normalization and Centroid Alignment . . . . . . . . . . . . . . .
26
2.2: HMM approach of training and classification . . . . . . . . . . . . . . . . . . . . . . .
30
2.2.1: Discrete Hidden Markov Model Introduction . . . . . . . . . . . . . . . . . .
31
2.2.1.1: Elements of HMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.2.1.2: Three Basic Problems for HMM . . . . . . . . . . . . . . . . . . . . . . .
34
2.2.1.3: Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.2.1.4: Optimal State Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.1.5: Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.2: HMM Operation steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.2.1: Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.2.2: Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.2.2.3: HMM Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2.2.2.3.1: Model Optimum Parameter estimation . . . . . . . . . . . .
40
2.2.2.3.2: Optimum state sequence estimation . . . . . . . . . . . . . .
45
2.2.2.4: HMM Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
2.2.2.4.1: The Forward Procedure . . . . . . . . . . . . . . . . . . . . . . . .
48
2.2.2.4.2: The Backward Procedure . . . . . . . . . . . . . . . . . . . . . .
52
2.3: Approach of Combination between ETMF and HMM . . . . . . . . . . . . . . . .
53
2.3.1: Motivation for Hybrid approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
2.3.2: Proposed Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
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2.3.2.1: Necessity of developing modified hybridization in ETMF ATR
56
2.3.2.2: Number of Subset Model selection and Weight calculation . . .
58
2.3.2.2.1: Subset Model Selection . . . . . . . . . . . . . . . . . . . . . . . .
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2.3.2.2.2: Weight determination . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4: Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4.1: Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4.2: ETMF Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4.2.1: Formation of Template Profiles . . . . . . . . . . . . . . . . . . . . . . . .
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2.4.2.2: Classification using Matched Filter Technique . . . . . . . . . . . .
65
2.4.3: HMM Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.4.3.1: Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.4.3.2: Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.4.3.3: Training and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
2.4.4: Single Look Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
2.4.4.1: Forced Decision Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
2.4.4.2: Classification in Unknown Target Scenario . . . . . . . . . . . . . . .
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2.4.4.3: Computational Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.4.5: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3: Time Recursive Multiple Hypothesis Testing
88
3.1: Theory Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
3.2: Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
3.2.1: ETMF classifier Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . .
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92
3.2.1.1: Description of MSTAR Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
3.2.1.2: Multilook Performance Results . . . . . . . . . . . . . . . . . . . . . . . . .
93
3.2.2: Hybrid Classifier Simulation results . . . . . . . . . . . . . . . . . . . . . . . . .
95
3.2.3: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4: Improved SAR Target Detection Using Subspace Filtering
99
4.1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
100
4.2: Ultra-wideband Radar simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103
4.3: Eigen-Analysis of SAR image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
4.4: Clutter Suppression Capability of SVD . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
4.5: SVD based SAR Target Detection Algorithms . . . . . . . . . . . . . . . . . . . . . .
108
4.5.1: Energy Normalized SVD (EN-SVD) . . . . . . . . . . . . . . . . . . . . . . . . .
108
4.5.1.1: Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
108
4.5.1.2: EN-SVD Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
4.5.1.3: EN-SVD Testing Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
4.5.2: Condition-Statistic SVD (CS-SVD) . . . . . . . . . . . . . . . . . . . . . . . . . .
114
4.5.3: Terrain-Filtered SVD (TF-SVD) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
4.5.3.1: Motivation and Kernel formation . . . . . . . . . . . . . . . . . . . . . . . .
115
4.5.3.2: Implementation steps of TF-SVD . . . . . . . . . . . . . . . . . . . . . . .
118
4.5.4: Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
4.5.4.1: UWB SAR simulated image specification . . . . . . . . . . . . . . . .
120
4.5.4.2: Performance Comparison of Target Detection algorithms . . . .
122
4.5.4.2.1: Performance Comparison in Offline training mode . .
122
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4.5.4.2.2: Performance Comparison in Self-Training mode . . . .
129
4.5.4.3: Performance Comparison of various techniques . . . . . . . . . . .
132
4.5.4.4: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
5: Summary and Future work
137
5.1: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
137
5.1.1: Hybrid ATR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
137
5.1.2: Time Recursive Sequential ATR . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.1.3: SAR target detection algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
5.2: Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140
141
Bibliography
ix
List of Figures
1.1
Side looking radar system geometry . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.1
Eigen-Template Generation from detected HRR profiles . . . . . . . . . . .
21
2.2
Distribution of Singular values for MSTAR target T72, 1000 sector . . .
23
2.3
Implementation of the Correlation Classifier . . . . . . . . . . . . . . . . . . . . .
25
2.4
Observation and Template Profiles are shown in shaded and blank
27
boxes of different lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5
Shift = -8 of Centroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.6
Shift = 0 aligned of Centroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.7
Shift = +8 of the Centroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.8
Simplified Block diagram of target recognition using HMM . . . . . . . .
30
2.9
Two states Hidden Markov Model with two output symbols, V1 and
32
V2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10
Flow diagram for LBG clustering algorithm . . . . . . . . . . . . . . . . . . . . .
2.11
Illustration of the sequence of operation required for the computation of the joint event that the system is in state Si at time t and state Sj at
38
43
time t+1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12
Baum-Welch learning algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
44
2.13
Block Diagram of a Designed HMM recognizer . . . . . . . . . . . . . . . . .
2.14
Illustration of the sequence of operations required for the computation
47
of the (a) forward variable and (b) backward variable . . . . . . . . . . . . . .
49
2.15
State lattice used to derive the forward/backward recursion . . . . . . . . .
51
2.16
Data flow in the proposed hybrid algorithm . . . . . . . . . . . . . . . . . . . . .
57
2.17
In 100 aspect case, this plot shows the HMM recognition rate with
60
number of HMM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.18
This figure is used to determine the most effective W1/ W2 so that the
62
combined ETMF+HMM recognition rate is the highest . . . . . . . . . . . . 2.19
Bar plot representation of ETMF, HMM and Hybrid classifier
72
performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.20
ROC curves for Probability of declaration vs Conditional Probability
78
of Correct Classification (Single profile) . . . . . . . . . . . . . . . . . . . . . . . . 2.21
ROC curves for Probability of False Alarm vs Probability of
78
Declaration (Single profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.22
ROC curves for Probability of declaration vs Conditional Probability
80
of Correct Classification (3 profile average) . . . . . . . . . . . . . . . . . . . . . 2.23
ROC curves for Probability of False Alarm vs Probability of
80
Declaration (3 profile average) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.24
ROC curves for Probability of declaration vs Conditional Probability
81
of Correct Classification (5 profile average) . . . . . . . . . . . . . . . . . . . . . 2.25
ROC curves for Probability of False Alarm vs Probability of Declaration (5 profile average) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
81
2.26
ROC curves for Probability of Declaration vs Conditional Probability
82
of Correct Identification (Combined result) . . . . . . . . . . . . . . . . . . . . . . 2.27
ROC curves for Probability of False Alarm vs Probability of
82
declaration (Combined result) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.28
ROC curves for Probability of False Alarm vs Conditional Probability
83
of Correct Classification (Combined result) . . . . . . . . . . . . . . . . . . . . . 3.1
Block diagram for time recursive multiple hypothesis Combiner . . . . .
91
3.2
ROC curves for Probability of detection vs Conditional Probability of
93
Correct Classification (time recursive ETMF) . . . . . . . . . . . . . . . . . . . . 3.3
ROC curves for Probability of False Alarm vs Probability of
94
declaration (time recursive ETMF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4
ROC curves for Probability of False Alarm vs Probability of
95
declaration (time recursive hybrid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5
ROC curves for Probability of Declaration vs Conditional Probability
96
of Correct Identification (time recursive hybrid) . . . . . . . . . . . . . . . . . . 3.6
ROC curves for Probability of False Alarm vs Conditional Probability
96
of Correct Identification (time recursive hybrid) . . . . . . . . . . . . . . . . . . 4.1
Block Diagram for UWB SAR Simulation . . . . . . . . . . . . . . . . . . . . . .
102
4.2
Eigen Spectrum of Target and Clutter blob . . . . . . . . . . . . . . . . . . . . . .
110
4.3
SAR image feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
111
4.4
Filter kernel for “Terrain-Filtered SVD” . . . . . . . . . . . . . . . . . . . . . . . .
116
4.5
Sample Filter Histogram for TF-SVD . . . . . . . . . . . . . . . . . . . . . . . . . .
117
xii
4.6
Sample UWB SAR Simulation test Image . . . . . . . . . . . . . . . . . . . . . . .
119
4.7
Sample UWB SAR Simulation Clutter only image . . . . . . . . . . . . . . . .
120
4.8
UWB SAR simulation image after performing EN-SVD . . . . . . . . . . .
122
4.9
UWB SAR simulation image after performing CS-SVD . . . . . . . . . . . .
124
4.10
UWB SAR simulation image after performing Euclidean masking
125
operation in TF-SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11
Final UWB SAR simulation image after performing TF-SVD . . . . . . .
126
4.12
Performance comparison of EN-SVD, CS-SVD and TF-SVD in
127
offline training-real time testing mode . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13
Performance comparison of EN-SVD, CS-SVD and TF-SVD shown
128
in logarithmic scale in offline training-real time testing mode . . . . . . . 4.14
Performance comparison of EN-SVD, CS-SVD and TF-SVD in self-
130
train mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15
Performance comparison of EN-SVD, CS-SVD and TF-SVD in self-
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train mode (logarithmic scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.16
ROC Performance comparison of various techniques . . . . . . . . . . . . . .
133
4.17
ROC Performance comparison of various techniques (logarithmic
134
scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
List of Tables
I
Organization of a Confusion Matrix . . . . . . . . . . . . . . . . . . . . . . . .
68
II
Summary of Forced Decision Results . . . . . . . . . . . . . . . . . . . . . . .
69
III
Confusion matrix for ETMF with single profile testing . . . . . . . . .
69
IV
Confusion matrix for HMM with single profile testing . . . . . . . . .
69
V
Confusion matrix for Hybrid algorithm with single profile testing .
70
VI
Confusion matrix for ETMF with three profile average testing . . . .
70
VII
Confusion matrix for HMM with three profile average testing . . . .
70
VIII
Confusion matrix for Hybrid algorithm with three profile average
70
testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX
Confusion matrix for ETMF with five profile average testing . . . .
70
X
Confusion matrix for HMM with five profile average testing . . . . .
70
XI
Confusion matrix for Hybrid algorithm with five profile average
71
testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII
Evaluation parameter computation from the confusion matrix . . . .
74
XIII
Confusion matrix (Unknown rejection threshold about 0.6) for
75
ETMF based classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIV
Confusion matrix (Unknown rejection threshold about 0.6) for Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
76
XV
Confusion matrix (Unknown rejection threshold about 0.6) for
76
ETMF based classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVI
Confusion matrix (Unknown rejection threshold about 0.6) for
76
Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII
Confusion matrix (Unknown rejection threshold about 0.6) for
77
ETMF based classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVIII
Confusion matrix (Unknown rejection threshold about 0.6) for
77
Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIX
Conditional Probability of Correct Classification of Hybrid and
84
ETMF classifiers at Pd = 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XX
Probability of Declaration of Hybrid and ETMF classifiers at Pfa =
84
0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXI
Conditional Probability of Correct Classification of Hybrid and
85
ETMF classifiers at Pfa = 0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXII
Improvement of Probability of Declaration of Hybrid classifiers
97
due to time recursive multilook approaches at Pfa = 0.4 . . . . . . . . . XXIII
Improvement of Conditional Probability of Correct Classification
97
of Hybrid classifiers due to time recursive multilook approaches at Pd = 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXIV
Improvement of Conditional Probability of Correct Classification of Hybrid classifiers due to time recursive multilook approaches at Pfa = 0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
97
ACKNOWLEDGEMENTS It is my pleasure to acknowledge and thank people who helped me accomplish my goal to pursue graduate studies. First I would like to thank my parents, Goutam K. Paul and Sipra Paul, for their constant support and encouragement. They have made lots of sacrifices to help me with my education, for which I will always be grateful. I would like to thank Professor Arnab K. Shaw, WSU, and Dr. Atindra K. Mitra, WPAFB/SNRR, for their guidance and encouragement throughout my thesis. I would also like to thank Dr. Kefu Xue and Dr. Fred Garber for agreeing to be on my thesis committee. I would also like to thank Thomas L. Lewis, WPAFB/SNRR for assisting me to generate the simulated target-clutter image. I would like to acknowledge my friends, Koel Das and Sivaram Bandaru for helping me with my thesis preparation. Lastly, I would wish to thank all the faculty members of the Electrical Engineering Department at Wright State University for their generous help and tremendous support through the course of my M.S. program.
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1: INTRODUCTION The objective of Automatic Target Recognition (ATR) algorithms is to correctly identify an unknown target from sensed radar signatures [1-4], whereas in target detection case, the requirement is to detect target from clutter. The need for ATR and target detection technology is evident from various “friendly fire” incidents. The most popular algorithm for ATR is the template-matching algorithm. Given a sensed signature from an unknown target, the ATR systems compare the observed signatures with a set of stored target hypotheses. The target decision is based on some form of optimum similarity between the observed signature and one of the stored targets. Template based ATR provides encouraging results as demonstrated in the work of Novak, et al. [5], Mirkin [6] and many others [7-9]. Whereas in target detection case, the classifier is trained to determine the threshold, which is a discriminant factor between target and clutter. Based on this threshold the classifier will perform target detection while nullifying clutter. In the next subsections a brief review of ATR/target detection and its background and previous work are depicted.
1.1: ATR/Target Detection Overview 1.1.1: A Review of ATR/Target Detection The present era of limited warfare demands precision strikes for reduced risk and cost efficient operation with minimum possible collateral damage. In order to meet such
1
exacting challenges, Automatic Target Recognition (ATR)/Target Detection capability is becoming increasingly important to the Defense community. The overall goals are to analyze image data using digital computers in order to detect, classify and recognize target signatures automatically, i.e., with minimum possible human assistance. The image data for processing may be generated by one of many possible imaging sensors including radar, optical, infrared or others. Hence target detection/recognition is considered to be one of the most challenging among current research problems because the system developers have little control over the possible target scenario and the operational imaging condition [14-17]. Also, compared to the diversity of possible images during operations, only a relatively smaller subset of images may be available at the development or training stage. Furthermore, the operational target detection/recognition algorithms may have to deal with intelligent adversary attempting to defeat the system, as opposed to amore controlled environment during development. Traditionally, air to ground acquisition of ground target information is categorized into two general areas: Moving Target Indication (MTI) and Synthetic Aperture Radar (SAR) [18-22]. The original purpose for developing these radar technologies had been to achieve all weather and all day/night imaging, i.e., to transcend traditional photographic camera based imaging that must rely on sunlight and is susceptible to clouds, fog or precipitation.
1.1.2: Moving Target Indicator (MTI) Most surface and airborne radar systems operate in an environment where the clutter return obscures targets of interest [23]. If the target is moving relative to the clutter it is
2
possible to filter out the undesired clutter return by exploiting the differential doppler frequency shift produced by relative target to clutter radial motion. Systems following this principle are called Moving Target Indicator (MTI) radar. MTI has the capability to detect target reflections [24] having differential radial motion with respect to the clutter. The clutter causing background may be either terrain, sea, weather or chaff [25-26]. MTI’s are operated with either fixed based or a moving platform such as an aircraft or a satellite. Considering detection of low flying aircraft’s, i.e. the radar is surface based, flying over terrain through possible weather disturbances. In such an event, MTI rejects the returns from terrain and weather while retaining the return from the aircraft. This property gives it good detection capabilities for air borne targets. In cases where the target is surface based, as in Air to Ground ATR application, the ground clutter are stronger than the expected target return.
The ground clutter
extends out to a range where terrain features that cause the clutter are masked due to earth's curvature. In such cases, the ground clutter extends to the full operating range of the radar. This makes MTI without any recognition capabilities. MTI is a mature radar technology that allows airborne sensors to survey large areas of land and it has coarse target detection and range determination capabilities. It makes use of target movement for image formation and hence, it is highly effective for distinguishing moving targets from ground clutter. However, a major drawback of the MTI technology is its lack of any target recognition capability.
3
1.1.3: Synthetic Aperture Radar (SAR) Although the major emphasis of this thesis is to utilize HRR profiles, as described in the previous chapter, it may be pointed out here that data collection as well as most of the front-end processing for HRR is identical to that of SAR. Hence, in this Section, SAR image formation is described in considerable detail. Figure 2.1 shows the side-looking radar system wherein an aircraft carry on-board a SAR imager [27-28] illuminates a patch of ground having a target with certain surroundings. The beam of the radar looks out to the side of the aircraft, in a direction orthogonal to its flight path. This direction of radiation propagation is referred to as the Range direction and the direction parallel to flight path is called the Cross-range direction. During the aircraft's movement, it periodically transmits pulses of microwave energy that impinge on the patch containing the target. Each of these pulses is subsequently reflected back to and received by the radar, where demodulation is performed. The assemblage of data collected and pre-processed in this manner is called a phase history and is passed on to the processor for image reconstruction. The processor could either be located on the ground or on board the flying aircraft. This processor gives out as output the electromagnetic reflectivity of the illuminated ground patch. The reflectivity is a two-dimensional function having dimensions as Range and Cross-range. Although a SAR picture looks entirely different from an optical photograph, the key features are easily recognizable. SAR is coherent radar that employs signal processing and motion compensation to provide a high spatial resolution estimate of the scenes reflectivity, also commonly known as Radar Cross Section (RCS). Motion sensors are used to measure platform flight characteristics so that non-ideal flight path generated
4
phase errors can be removed during image formation processing. Platform or target motion creates scene aspect variations, leading to a differential doppler signature of scatterers in the antenna footprint. The doppler signatures are subsequently exploited to achieve enhanced Cross-range resolution. Doppler frequency is 1/(2π(dφ/dt)), where φ = 4πR/λ. This is the fundamental behind SAR imaging concept (also commonly known as Range/Doppler imaging).
The reasons for using SAR images over optical ones are summarized below. •
It is able to image a surface with very fine resolution of a few meters to coarse resolution of a few kilometers.
•
It can provide imagery to a given resolution independently of altitude, limited only by the transmitter power available.
•
A number of fundamental parameters such as polarization and look angle can be varied to optimize the system for a specific application.
•
Imaging is independent of solar illumination (availability or angle) because the system provides its own source of illumination.
•
It can operate independently of weather conditions if sufficiently long wavelengths are chosen.
•
It operates in a band of electromagnetic spectrum different from the bands used by visible and infrared (IR) imageries.
5
1.1.4: High Range Resolution (HRR) MTI and SAR are active Doppler systems that transmit and receive electromagnetic waveforms in the microwave bands that have superior penetrating capabilities than visual frequency bands. These radar technologies are being researched and developed over several decades now and both concepts have some share of strengths and weaknesses. MTI makes use of target movement for image formation and hence, it is highly effective for distinguishing moving targets from ground clutter. It is a mature radar technology that allows airborne sensors to survey large areas of land and it has coarse target detection and range determination capabilities. However, although very useful for target detection, the MTI technology lacks target recognition capability. In case of SAR, in contrast, ground target information is available for processing in both range and cross-range domains, and it has excellent target recognition and identification capabilities. However, processing requirements for SAR is considerably high, preventing it from being used as a wide area surveillance technology. Unlike SAR and MTI, the HRR technology considered in this work would rely on processing high resolution `Range Profiles', as distinguished from traditional SAR-ATR that utilizes SAR image data. Its potential target recognition capability promises to bridge the gap between the wide area surveillance target detection capabilities of MTI and the very narrowly focused target identification capabilities of SAR. HRR images are used to overcome the disadvantages of SAR data whereas moving targets are concerned. In case of SAR images, the ability to achieve high CrossRange resolution is limited by the migration of scatterers into neighboring resolution cells.
6
Figure 1.1: Side looking radar system geometry
Secondly, even a Cross-Range resolution of 1 ft can require large angular aperture, resulting in significant blurring due to scattered migration. This becomes evident at low frequencies since a large coherent processing angle is required for a given Cross-Range resolution. Moreover, the image blurring becomes significant as the migration of scatterers approaches the desired resolution. All these factor make recognition hard for moving targets. In case of HRR profiles, all the information in range is still present, but the cross-range blurring is not present. This makes HRR as the most feasible choice as far as moving target is concerned and HRR radar sensor has wide application in target tracking.
7
1.2: Background and Previous Work Most research in the field of target recognition address data study, theoretical formulation and algorithm development. Clearly, important milestones [29-30] have been reached in these areas. However, barring some notable exceptions [31-33] most existing target detection/recognition algorithms are meant to be implemented using 2-D Synthetic Aperture Radar (SAR) image data. These algorithms are critically dependent on appropriate target and sensor models. The major limitation of detection/identification using SAR is its failure to recognize correctly in case of moving targets due to blurring caused in the Cross-range domain. This problem makes SAR-target recognition unsuccessful in case of moving targets. The other field in which much research is done is target detection/recognition using Moving Target Indicator (MTI). MTI radar is very good for detection but fails due to coarse recognition capabilities. In fact, most well established algorithms are mathematically and computationally so comprehensive that it would be quite impractical to implement those in on-line applications. This problem grows when the number of targets to be detected becomes large. The previous work on ATR encompasses a variety of approaches. SARdetection/estimation is one of the most important ones [34-36]. An accurate clutter model had been suggested for precise target detection [37]. The power spectral density (PSD) of the clutter was estimated such that a multi-dimensional matched filter could be designed for detection. Another approach [34] has been used for model-based ATR/detection techniques. The basic paradigm involves detection and feature extraction such that they can be used in hypothesis using target identities. If the hypothesis is satisfied, the target is termed as recognized else it is reformed and used to improve the predicted signature.
8
Morgan, et al. [35] has used the Classical Bayesian detection and decision theory for model-based ATR. It was proposed that when the model tends to represent the uncertainties in target type, shape, surround, scatterers and feature extraction, then classical theory yields model based ATR techniques. The concept was extended to use of model-based templates for SAR-ATR [36]. Mahalanobis [38] has discussed the use of a correlation filter in SAR-ATR at the recognition stage. The previous work on detection/recognition also includes using Multi-resolution Wavelet Decomposition [39-41]. The Wavelet Transform has been found to be highly effective for image analysis, data and image compression, feature analysis, and many other applications [42-44]. It has also been used for speckle reduction of SAR images [45]. Image compression is achieved by successive Wavelet Decomposition of the image using a pyramid scheme. Peterson et al. [46] has developed a technique for classifying different objects in natural imagery by employing a wavelet transform and training a neural network on certain wavelet transform coefficients in pattern recognition context. Tagaliarini et al. [47] also incorporated the use of Wavelets with Neural Networks. In his work, the filter coefficients are a linear combination of wavelet coefficients and can give rise to an energy distribution that makes recognition easier when compared with that of conventional wavelets. The use of Eigen vectors corresponding to an Eigen value problem has been extensively utilized in many applications like Sonar, SAR etc. Bottcher et al. [48] has presented the optimal method for term expansions based on the optimum eigen function related to surface of the object. Here, the conversion of Fredholms integral equation of first kind was done as an eigen value problem of a related hermition operator. This led to
9
target identification by solving the classical scattering theory of waves. Work on ATR has also been done using Hidden Markov Models (HMM). HMM has been found to be extremely successful in speech recognition [49] and it has also found some use in SAR target detection [50]. Liao et al. [8] extracted features from each of the HRR waveforms via the RELAX algorithm before feeding those to HMM. Another approach to detection/recognition is by computer simulation [51], wherein the elements of the complex system are implemented as interacting software objects. New methods have been proposed for use as these software objects. The target recognition is performed by a family of 2D cluster filters. Artificial Intelligence [52] has been used in ATR applications to reduce the search combinatorics. These methods use domain specific information for robust physical description of the images. HRR-ATR has been used to solve the problem of moving target recognition [5354]. ATR using HRR profiles has been tried using Neural Networks [55-56]. Yiding et al. used the property of the distinction of Doppler modulation echo for different targets in HRR profiles for target recognition. The echo spectral density is obtained by the Fourier transform. Following that, the choice of the total spectral energy and the four segment spectral energy as characters is done for use in Neural Networks for ATR. Xun et al. [55] have used the Matrix Pencil method for scattering centers extraction from full polarization multi-frequency scattering returns. Feature Extraction is done by using transient polarization response. Finally, the classification of selected features is done using Multi-resolution Neural Network. Worrell [56] has used the mean-based templates for feature extraction. Jacobs et al. [52] has chosen a deterministic Gaussian model for each Range profile. The likelihood functions under each model for varying orientations
10
and target types are compared. The limit on the orientation estimator performance is described in terms of Hilbert-Schmidt bound on the estimation error. Stewart et al. [57] has compared the different classification approaches for HRR profiles. The intrinsic dimensionality of the signatures was obtained using kth nearest neighbors. The two classifiers compared were the Gaussian classifier and synthetic discriminant function (SDF) classifier. In his work, he found that the Gaussian correlation classifier performed better in presence of white noise while the SDF approach worked better for large angle bin size. In a detection/estimation algorithm importance must be given to the fact that how the target orientation phase behaves to changes in the feature extraction, especially in case of moving targets.
1.3: Background on Automatic Target Recognition using HRR profiles For several years, Automatic Target Recognition has been studied for Moving Target Indicator (MTI) and Synthetic Aperture Radar (SAR) images. MTI and SAR are active Doppler systems that transmit and receive electromagnetic waveforms in the microwave bands that have superior penetrating capabilities than visual frequency bands. Though they are much superiors to optical images they have certain drawbacks when used for recognition of moving targets. MTI makes use of target movement for image formation and hence, it is highly effective for distinguishing moving targets from ground clutter but it lacks target recognition capabilities. In case of SAR, in contrast, ground target information is available for processing in both range and cross-range domains, and it has excellent target recognition and identification capabilities. However, processing
11
requirements for SAR is considerably high, preventing it from being used as a wide area surveillance technology. Moreover, the performance of SAR target detection algorithms degrade when the target is moving because SAR images cannot be formed properly for moving targets due to blurring caused in the cross-range domain. Unlike SAR and MTI, the HRR technology would rely on processing High Range Resolution (HRR) radar signatures, as distinguished from traditional SAR-ATR that utilizes SAR image data. The information contained in this signature is the radar scattering characteristics of the target as a function of range along the line of sight of the radar. It’s potential target recognition capability promises to bridge the gap between the wide area surveillance target detection capabilities of MTI and the very narrowly focused target identification capabilities of SAR. Also there is considerable saving in front end processing in HRR profile generation which require 1-D FFT operation as opposed to SAR’s use of 2-D FFT. The primary difficulty associated with the HRR sensor for ATR is that it collapses three-dimensional information into a single dimension, as opposed to 2D information in SAR, making HRR-ATR a more challenging task. Recently Target Detection using HRR profiles achieved lots of attention in literature. Nguyen et al. [7] developed a superresolution technique for HRR ATR with High Definition Vector Imaging (HDVI), where a super-resolution technique is applied to the HRR profiles before the profiles are passed through ATR classification. A statistical feature based classifier developed by Mitchell and Westerkamp [9] for robust HRR radar target identification showed that the amplitude and location of HRR signature peaks could be used as features for target classification.
12
Currently, one of the priority research initiatives of the Air Force is to develop an advanced air-to-ground HRR ATR program. The ultimate program objective is to transition mature HRR-ATR technology into operational Air Force airborne attack and surveillance platforms. The new HRR-ATR technology can be applied into a system approach and it is expected to vastly improve Air Force's ability to detect, recognize, as well as identify time-critical military targets. ATR performance with HRR is found to be excellent for stationary targets, as discussed in the later chapters. It is expected to be superior for moving targets which cause blurring Synthetic Aperture Radar (SAR) images making recognition a difficult task. Research on HRR-ATR requires a multifaceted approach is essential in order to harness recent advances from multiple disciplines.
At the initial stage, complete
characterization of the HRR-profile data was conducted encompassing both theoretical and implementation aspects. This included though not limited to, correlation analysis, histogram analysis, sector generation and matching, feature extraction, principal component analysis, signature generation, recognition using Matched Filtering and Least Squares. Once the interpretation of the basic characteristics of the HRR profiles was complete, the accumulated insights were eventually gathered systematically in the ATR algorithms developed. Different ATR approaches were studied to compare the performance of different algorithms. Our previous work [11-12,58-59] demonstrated that effective HRR-ATR performance can be achieved if the training templates are formed via Singular Value Decomposition (SVD) of detected HRR profiles and the classification is performed using Normalized Matched Filtering (MF). It was demonstrated in [11-12,58-59] that a
13
significant proportion (>90%) of target energy is accounted for by the dominant Eigenvector of the range-space correlation matrix. More interestingly, it was shown that the range and angle basis spaces are numerically decoupled in the form of left and right eigenvectors, respectively. This enabled us to exploit the decoupled range information exclusively for the purpose of target recognition. The theoretical results were also presented to demonstrate that the range space eigenvectors constitute the "optimal" features in the range domain. Basis space decomposition via SVD is also shown to be useful for suppression of clutter from measured profile data by eliminating the eigenvectors corresponding to smaller singular values, which represent noise or clutter sub-spaces. In [12], it was demonstrated certain limitations of the use of Power Transform when the observation profiles are noisy. Specifically, it was shown that significant signature information might be lost due to the application of Power Transform on detected noisy profiles, leading to considerable reduction in ATR performance. Hybridization of multiple optimization techniques has also been attempted for HRR ATR. In [58], the entire 360-degree of a target vehicle circumference was divided into several optimum-sized sub-targets and templates were constructed from these subtargets. Then the result of template matching was combined using Bayesian updating to arrive at the final target classification. Earlier research works on HRR-ATR focused on simulated XPATCH data [5960]. But this thesis concentrates on recognition of stationary targets using the MSTAR data.
14
1.4: Background on Target Detection on SAR images Synthetic Aperture Radar (SAR) imagery is commonly used as a tool in detecting, classifying, recognizing and possibly identifying mobile or stationary targets. Recognizing target from SAR images is an important, yet challenging application if the target is hindered under outliers. To date, the authors have engaged in research and published results on a number of approaches to target detection [11] in the ultrawideband (UWB) SAR area. The approaches presented include detailed discussion on a number of aspects of ultra-wideband radar target detection and algorithm development. A bi-modal technique for modeling ultra-wideband radar clutter was proposed. An approach to developing a new class of rank order filters, known as, “discontinuity filter” for ultrawideband radar target detection applications was presented. These approaches mainly concentrate on the investigation of algorithms that implement elaborate off-line training as well as the development of rank-order filtering algorithms that are designed for basic UWB SAR sensor phenomenology and at the same time do not require an extensive offline training step. Both of these approaches have been shown to generate an acceptable level of performance under certain conditions that are of interest for UWB SAR applications.
1.5: Thesis Contribution In this thesis HRR-ATR performance has been analyzed for Moving & Stationary Target Acquisition and Recognition (MSTAR) data using hybridization of Hidden Markov Model (HMM) and Eigen Templates based Normalized Matched filter (ETMF) based ATR algorithm. The following contributions were made to the existing ATR techniques:
15
A new hybrid 1-D ATR approach is presented where the HRR test profiles are first scored by ETMF and then the most likely HMM models determined by ETMF are used for HMM scoring at the second step. Final ATR decision is based on proper weight combination of the two individual scores. Performance comparison results are provided for Forced Decision as well as for Unknown Target scenarios. The unknown target scenario is simulated using the Leave One Out Method (LOOM) [4]. The performances of ATR algorithms are compared in terms of the Receiver Operating Characteristics (ROC) curves.
In this paper, the proposed hybrid algorithm is extended for moving target case, which will facilitate simultaneous, multiple target tracking. For Continuous-ID and joint tracking, the single look ETMF and HMM hybrid technique needs to be applied time-recursively to update the multiple ID hypothesis as new range profiles are observed over time. The proposed approach would be a recursive version of the block-processed stationary multi-look approach [2] that has shown considerable success in identifying stationary targets.
In addition to ATR, considerable improvement in SAR target detection field is also performed.
A set of results from an investigation of an approach denoted as “self-training algorithms for ultra-wideband SAR target detection” is presented. Under this
16
approach, a number of categories of algorithms are investigated that implement “selftraining” procedures. These procedures are developed such that a set of localized regions within a given SAR image are sampled in real-time for purposes of obtaining low-order and robust real-time clutter models. These real-time models are applied in a sliding-window type target detection paradigm for clutter cancellation and target detection.
Results are presented from the analysis of three new categories of
algorithms that were developed specifically for this investigation.
These three
categories of algorithms denoted as “Energy-Normalized SVD” (EN-SVD), “Condition-Statistic SVD” (CS-SVD), and “Terrain-Filtered SVD” (TF-SVD) are generating satisfactory simulation results for severe UWB SAR impulsive-type clutter. Though offline training is required for both EN-SVD and CS-SVD to perform satisfactory level, the third approach TF-SVD is a notable step to develop a self training algorithm system i.e. where no offline training is required and the algorithm will learn as it flies on the observation image.
1.6: Thesis Outline A brief overview of the thesis is as follows: Section 2 describes the hybrid approach of ETMF and HMM. Section 2.1 gives a brief description of ETMF approach; section 2.2 provides a brief overview of HMM training and classification. Section 2.3 explains in detail the process of combining between ETMF and HMM. Section 2.4 provides the HMM simulation parameters and also shows the ATR performance results for both ETMF and HMM individually and the resulting hybrid technique. Section 2.5 summarizes the results obtained.
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Section 3 is devoted to explore the performance capability of the proposed time recursive multiple ID hypothesis. Section 3.1 briefly summarizes the approach and assumptions, Section 3.2 compares the performance between single profile hypothesis and time recursive multi profile hypothesis. Section 3.3 summarizes the performance improvement due to time recursive target ID updating approach. In Section 4 a number of methodologies to develop a “self-training” algorithms for UWB radar target detection are investigated. The SAR simulation algorithm is discussed in detail in section 4.1. A brief discussion of eigen analysis on SAR and clutter suppression capability of SVD are presented in section 4.2. The “Energy-Normalized SVD”, “Condition-Statistic SVD”, and “Terrain-Filtered SVD” algorithms are discussed in section 4.3 and comparative detection results are presented in section 4.4 along an analysis and discussion. Section 5 presents the conclusion, possible future application and the summary of this work.
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2: Robust HRR Radar Target Identification by Hybridization of HMM and Eigen Template based Matched Filtering
A new hybrid Automatic Target Recognition (ATR) algorithm is developed for sequential HRR radar signatures. The proposed hybrid algorithm combines ETMF and HMM techniques to achieve superior HRR-ATR performance. In the proposed hybrid approach, each HRR test profile is first scored by ETMF which is then followed by independent HMM scoring. The first ETMF scoring step produces a limited number of “most likely” models that are target and aspect dependent. These reduced number of models are then used for improved HMM scoring in the second step. Finally, the individual scores of ETMF and HMM are combined using Maximal Ratio Combining to render a classification decision. Classification results are presented for the MSTAR data set via ROC curves.
2.1: ETMF Approach of training and classification In ETMF approach of target classification, a new air-to-ground HRR-ATR algorithm is proposed, where the template features are obtained via Singular Value Decomposition (SVD) of HRR profiles and the unknown target classification is performed using normalized Matched Filtering. The SVD operation projects the information content in a detected HRR profile matrix onto orthogonal basis spaces. This
19
is also known as Karhunen-Loeve Transformation or Principal Component Analysis. More interestingly, when SVD is applied to a HRR profile matrix, which is range vs. aspect, it is shown that the range and angle basis spaces are numerically decoupled in the form of left and right eigen vectors, respectively. This enables us to exploit the decoupled range information exclusively for the purpose of target recognition. The Theoretical results presented in [11-12] demonstrated that the range-space eigen vectors constitute the "optimal" features in the range domain. In addition, SVD analysis of a large class of MSTAR targets indicates [12] that over 95% of target energy is accounted for the largest singular value only, further justifying the proposed utilization of significant range-space eigen-vectors as templates. Basis space decomposition via SVD is also shown to be useful for suppression of clutter from measured profile data by eliminating the eigen-vectors corresponding to smaller singular values, which may represent noise or clutter sub-spaces.
2.1.1: HRR Data Generation and Preprocessing Most work on Automatic Target Recognition (ATR) has been performed using Synthetic Aperture Radar (SAR) images. ATR using SAR images performs poorly in case of moving targets due to blurring caused in the cross-range domain. The HRR-ATR technology relies on processing high resolution 'Range Profiles', as distinguished from traditional SAR-ATR that utilizes SAR image data. In HRR based ATR systems there is a considerable saving in front-end processing in producing HRR profiles which require only 1-D FFT operation, as opposed to SAR's use of 2-D FFT. The processing factor becomes significant in case of on-line processing because in order to produce a single
20
SAR image, radar returns must be generated over a relatively large sector of angles. With HRR profiles, only a relatively small number of angles would be sufficient to perform ATR. Figure 2.1 shows the process of generating HRR profiles from Complex Phase History (CPH). As shown, SAR image can be obtained from the HRR profiles by taking Fourier transform in the angle-domain to produce the cross-range information. The Range Swath to be imaged is defined a-priori based on Altitude and depression angle of radar. This makes a fixed sampling window. The two primary HRR waveforms for SAR systems are the Frequency stepped and Linear Frequency modulation. The Range resolution (∆R) is determined by the radar RF bandwidth. Thus, the resultant received signal (Y ( τ j )) in each Range gate would be N
Y(τ j ) ∝
∑
σi e
j4 πR i λ
2
(2.1)
i =1
Where σi is the RCS of elemental scatterers in Range gate, Ri is the Range and N is the number of scatterers in a Range gate.
Complex phase history (CPH)
IFFT
Complex HRR
(r2+x2)1/2
Detected HRR profiles
SVD
Fig. 2.1: Eigen-Template Generation from detected HRR profiles
21
Eigen Templates
Note that no power transform operation is performed on magnitude HRR as in [12] we proved that, power transform severely degrade ATR performance if noise is embedded with Complex Phase History data.
2.1.2: Normalization The template profiles of all the targets are normalized to have same length (i.e. energy), while preserving their angular separation and relative variations in scattering returns.
2.1.3: Alignment of HRR Profiles in Range The HRR profiles of the Segmented Data set provided by AFRL (TRUMPETS) are not aligned in Range. Hence each Profile of 1-Degree Sector should be aligned with respect to each other. This alignment is achieved by taking a profile as a reference and shifting the adjacent profile till maximum correlation was achieved. This procedure is repeated until all the profiles in a sector have been aligned. Though this procedure of aligning the HRR profiles is fairly accurate, but it is not fully perfect.
2.1.4: Eigen-analysis of HRR data for training Singular Value Decomposition (SVD) is a very effective and robust tool for decomposing any matrix into orthogonal basis spaces. Let Y be an NXM of detected range profiles at M angular looks containing N range gates each. The SVD operation produces basis decomposition in the form of three matrices, •
Y ∈ ℜ NXM: Detected HRR Profile Matrix, N = No. of Range profiles and M = No. of Angular looks
22
M
Y → UΛV = SVD
T
∑λ u v i
i
T i
(2.2)
i =1
where, •
Range-Space (Left) Eigen Vectors : (Use as Features) U = EV[YYT ] = [u1 ......un ] ∈ ℜ
•
NXM
(2.3)
Angle-Space(Right) Eigen Vectors : (Discard) V = EV[Y T Y] = [ v1 ....v m ] ∈ ℜ NXM
•
(2.4)
Singular Values : Λ = Diagonal[λ11 ......λ MM ] ∈ ℜ NXM
•
(2.5)
Range and Angle sub-spaces are decoupled via SVD. Eigen Value Distribution 6
5
4 e d ut i n g a M
3
2
1
0
0
5
10
15 20 Number of Eigen Values
25
30
35
Fig. 2.2: Distribution of Singular values for MSTAR target T72, 1000 sector
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Where, EV[.] denotes the operation “Eigen-Vectors of”. For Range vs. Angle HRR data, the left eigen vectors (U) span the orthogonal basis space in the range domain while the right eigen vectors (V) span the angle space. The middle matrix Λ is diagonal containing M (N>M is assumed here) singular values in decreasing order, λ11 ≥ λ 22 ... ≥ λ MM , where λ ii denotes the weights associated with i-th eigenvector. Larger
Singular values imply significant contribution of that particular eigen-vector in forming the target signal. Hence these are denoted as “signal subspace” eigenvectors whereas those corresponding to the smaller singular values are denoted as “noise or clutter subspace”. Figure 2.2 displays the distribution of singular values for a typical MSTAR targets in a particular degree range. In that case, it is seen that only the highest singular value ( λ11 ) makes up more than 96% of the total energy of the distribution. Interestingly the range space in U and the angle space eigenvectors in V appears in decoupled form after the SVD operation is applied to Y as shown in equation (2.3). It can be concluded, the HRR profile matrices are close to rank one, which implies that u 1 , the lefteigenvector corresponding to the largest (or dominant) singular value ( λ1 ) ought to contain the essential range information of the underlying target. Hence, here it is proposed to use the dominant range-space (left) eigenvector as the feature template.
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2.1.5: Unknown Target Classification
Template
||| Test Profile (shift = -8)
|| Test Profile (shift = 0)
|| Test Profile (shift =+ 8)
Fig. 2.3: Implementation of the Correlation Classifier
The unknown target classification is performed using Normalized Matched Filtering. Given observed (or, test) range profile(s) of an unknown target, the ultimate objective of classification is to determine which target class it belongs to. This is accomplished by comparing the observed profile with all the available templates, which are assumed to have been formed beforehand using training data set. The decision determines the target type for which the correlation between its template ( mi ) and the observation (a) profile is maximized among all template choices. However as the observation profile a and all the template may not be exactly aligned, the correlations have to be calculated with various lag values and the maximum correlation among all lags for each target type has to be determined. For each target, there are usually a large
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number of templates at different aspects. In our simulations with MSTAR database, correlation lag values up to ±8 were used. The maximum correlation value among all templates within ± D° of target aspect (assumed known or estimated by an MTI tracker) for each target is determined. This process is repeated for all target classes, with each class being assigned its maximum correlation out of all lags for aspect angles within ± D° . Finally, the target class having the maximum correlation value among all classes is termed the matched target class. In our simulations, correlation lag values up to ±5o of the true aspect was used because it is assumed that the MTI tracker (running in conjunction with HRR-mode radar) would provide a reasonably good aspect estimate.
2.1.6: Modified Normalization and Centroid Alignment To improve the performance of the ATR algorithm it is important to include that portion of the Observation and Template profiles which contains significant portion of the target signature information. Therefore, if the Observation and Template profiles are not prealigned it is important that they be aligned prior to using them in the classifier. In this work the Centroid of a range profile was used as the reference in aligning the Observation and the Template profiles. As described in the previous section, the Matched Filter Classifier assumes that both the Observation and the Template profiles are normalized to have equal lengths. However, while correlating the template and test profiles to find the best match, one of the profile vectors is shifted to the left and right of the Centroid to obtain the maximum correlation. When the observation profile is shifted over the Template profile, the region
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of overlap between the two would change with each shift. However, the norms of the overlapped regions of the observation and template may also change with each particular shift. Hence, using a stored template profile originally normalized over its entire length will not be appropriate if used as is. In order to satisfy MF’s requirement that both template and observation have identical lengths, it is important that only the overlapping parts of both the profiles is normalized prior to correlating the vectors, as described next. Let the test and template profiles be represented by narrow (shaded) and wide rectangles, respectively, as depicted in Figure 2.4. The lengths are shown different intentionally, as the test and template could be of different lengths. Different heights are used primarily to differentiate between the test and template. It has no other implication.
A Template Profile
OBSERVATION PROFILE
Fig. 2.4: Observation and Template Profiles are shown in shaded and blank boxes of different lengths
Next for better understanding, the correlation process with overlap normalization is described in detail. The test profile was shifted over the template and correlated. In the next figure, it is assumed that the shift is –8 with respect to the centroid. Clearly, the entire lengths of neither test nor the template are overlapping. Hence, it doesn’t make any sense to normalize over entire lengths of the template or test, because the correlation is
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occurring only over the overlapped (shown in stripe) region. It will be more appropriate to ensure that the norms within the overlap region of the vectors are kept the same. Hence, we re-normalize both vectors only over the overlapped parts (in stripe) before we perform correlation.
Overlap region to be normalized
Fig. 2.5: Shift = -8 of Centroid
Next, the case when both test and templates are aligned on the Centroid is depicted. In this case, the entire length of the template is overlapping some middle portion of the test. Hence, once again, we re-normalize only within the overlapping regions to ensure that both vectors have same lengths. It may be noticed that the length of the overlapped portion (in stripe) of the vectors is longer than the previous case.
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Overlap region to be normalized
OVERLAP REGION
Fig. 2.6: Shift = 0 aligned of Centroid
Next, the +8 shift case from centroid is shown. Again, the overlapped regions have changed for both. Again, only the striped regions are normalized for both vectors before correlating.
Overlap region to be normalized
Fig. 2.7: Shift = +8 of the Centroid
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2.2: HMM approach of training and classification Some recent work has shown encouraging promise for the use of HMM in HRR target recognition [8]. The airborne radar transmits microwave pulses at constant depression angle. Each pulse is reflected from the target and gets back to the radar receiver. Preprocessing is performed on the scattered waveforms and the output achieved is sequence of range scattered pulses which is termed as High Range Resolution (HRR) profiles. The HRR signatures characterize the target at a specific airborne sensor orientation. In the MSTAR data collection studies, it is assumed that the depression angle of airborne radar with respect to the target is constant and the target sensor orientation is modeled as the change of azimuthal orientations. Though there is significant variability in HRR signatures at different orientations, the scattered range field can be assumed to be stationary over small angular sectors. Each such angular region is termed as a “state”. As the target orientations are unknown in addition to target identity, theses information can be assumed as hidden and HMM can be used to model and characterize the sequence of scattered waveforms. Figure 2.8 shows a framework for HRR-based target recognition using HMM. HRR profiles (Training data)
Training
Model (HMM)
Code Book
HRR profiles (Test data)
Target Classification
Testing
Fig. 2.8. Simplified Block diagram of target recognition using HMM
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This subsection describes an introduction to Hidden Markov Models and algorithms for evaluation, HMM training using Forward-Backward algorithm and HMM classification using maximum likelihood viterbi searching.
2.2.1: Discrete Hidden Markov Model Introduction It is often convenient to think of HMM as a collection of interconnected states. Like the classical Markov model, we use a transition probability to provide the probability of a transition from one state to another. Unlike a classical Markov model, a Hidden Markov Model introduces an output probability density function (Pdf) to define the conditional probability that a symbol is generated from a finite set of symbols, given that we are in a particular state. From the probabilistic perspective, HMM’s characterize a stochastic process with an underlying Markovian finite-state structure that may only be observed indirectly (hence the “hidden” nature of the model). At any given time, it is unknown to an outside observer what state the process is in, but it can be observed through the sequence of symbols emitted from the states. We will limit our consideration to the first-order Hidden Markov Model, where state dependencies are on the immediate predecessor only. Another assumption made in this discussion is output-independence, which means the output symbol probability depends only on the current state at this observation frame and is conditionally independent from the previous state and the past symbols emission. This second assumption may degrade the experimental realism of HMM’s, but it reduces the number of parameters required by the model and allows the use of efficient evaluation and training algorithms in the synthesis and learning phase.
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2.2.1.1: Elements of HMM
Fig. 2.9: Two states Hidden Markov Model with two output symbols, V1 and V2
Figure 2.9 shows a Hidden Markov Model with two output symbols, V1 and V2. This simple model is used to explain the elements of HMM. The parameters of the HMM that can generate the output symbols V1 and V2 are shown in Equation (2.6) and (2.7).
N = 2, M = 2
(2.6)
1 0.6 0.4 0.8 0.2 π = , A = , B= 0 0.2 0.8 0.3 0.7
(2.7)
Following are the definitions for each parameter: N: the number of states in the model. We will denote the individual state as S = {s1 ,s 2 ,s 3 ,...s N } , and the state at time t as qt.
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M: the number of distinct observable symbols per state or the size of the codebook.
We denote the individual symbols as V = {v1 , v 2 , v3 ,..., v M } , and the observation symbol at time t as Ot. A: NxN matrix representing the state transition probabilities, i.e. the probability to
make a transition from state si to state sj: A = {a ij} where a ij = prob ( q t = s j | q t -1 = s i ) 1 ≤ i, j ≤ N
(2.8)
And
a ij ≥ 0,
N
∑a
ij
= 1 ,1 ≤ a ij ≤ N
(2.9)
j=1
B: NxM matrix which specifies the observation symbol probability distribution in the state sj: B = {b j (k)} where b j (k) = prob(v k = t | q t = s j ), 1 ≤ j ≤ N, 1 ≤ k ≤ M
(2.10)
And b j (k) ≥ 0,
M
∑ b (k) = 1 , k =1
j
1≤ j≤ N
(2.11)
π: N-element vector indicating the initial state probability distribution: π = {πi } , where πi = prob(q1 = si ), 1 ≤ i ≤ N
(2.12)
The complete parameter set λ of HMM requires the specification of two model parameters (N and M), the specification of the observation symbols, and the specification
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of the three probability matrices A, B and π. The compact but convenient notation is used to represent the parameter set of HMM model. λ = ( A, B , π )
(2.13)
2.2.1.2: Three Basic Problems for HMM The use of HMM models in real-world applications requires the solution of the following three problems related to the set of their parameter descriptors:
Probability Evaluation: Given a model and a sequence of observations, how do we efficiently evaluate the probability that the model generated the observations?
Optimal State Sequence: Given a model and a sequence of observations, how do we determine an optimal state sequence in the model that generated the observations?
Training: Given a model and a set of observations, how do we adjust the model parameters of λ to maximize the probability of generating the observations? In the following sections, the solutions proposed for each of these three basic problems are reported.
2.2.1.3: Model Evaluation The evaluation problem can be stated as: given the observation sequence
O = O 1O 2 ...O T , and a HMM model λ = ( A, B, π ) , compute P (O λ ) , the probability that the observed sequence is produced by the model. The most straightforward way to compute this is to enumerate all possible paths (state sequences) of length T that generate observation sequence O i.e. sum of all their probabilities.
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P ( O | λ ) = ∑ P ( Q | λ ) P ( O | Q, λ )
(2.14)
all Q
Where Q is the state sequence: Q = q1q 2 L q T and q1 is the initial state. The first factor in Equation (2.14) can be re-written by applying the two Markov assumptions: T
P ( Q | λ ) = ∏ P(q t | q t −1 ) = πq1 a q1q 2 a q 2q 3 L a q T−1qT
(2.15)
t =1
The second factor in Equation (2.14) can be re-written by applying the outputindependence assumption: P ( O | Q, λ ) = bq1 ( O1 ) ⋅ b q 2 ( O 2 ) L bq T ( OT )
(2.16)
Substituting Equation (2.16) and (2.15) into (2.14), we have: P ( O | λ ) = ∑ P ( Q | λ )P ( O | Q, λ )
(2.17)
all Q
=
∑
q1 ,q 2 ,...q T
πq1 b q1 (O1 ) a q1q2 b q2 (O 2 )...a qT−1qT b qT (O T )
(2.18)
From Equation (2.18) we can directly calculate the P (O λ ) from the HMM parameters, but the computation is unfeasible even for small values of N and T because the computational complexity increases exponentially with T. Fortunately, because of our assumptions, there is a more efficient algorithm called Forward-Backward procedure to compute P (O λ ) recursively.
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2.2.1.4: Optimal State Sequence
Given a model λ and a sequence of observations O = O1O2 ...OT , one problem that needs to be addressed is the estimate of the best state sequence Q = q1q 2 ...q T (or the most likely state path) corresponding to the given observation sequence. A dynamic programming method called Viterbi algorithm [60] is used to choose the optimal state sequence, i.e., to maximize P (Q O , λ ) , which is equivalent to maximizing P (Q, O λ ) .
2.2.1.5: Parameter Estimation
The training problem involves adjusting the model parameters in order to maximize the probability of the training observation sequences being produced by the model. The iterative procedure called the Baum-Welch algorithm is used to choose the maximum likelihood model parameter λ such that its likelihood function P(O | λ ) is locally maximized.
2.2.2: HMM Operation steps
2.2.2.1: Framing
Here, each HRR profile is blocked into frames of N samples, with adjacent frames being separated by M (M
