improved target recognition (book)

8/7/2019 Improved Target Recognition (book)

1/167

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


2/167

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 andTarget Detection Algorithms using HRR profiles and SAR images BE ACCEPTED INPARTIAL 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 onFinal 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


3/167

iii

ABSTRACT

Paul Anindya S. M.S.Eg., Department of Electrical Engineering, Wright State University,

2003: Improved Target Recognition and Target Detection Algorithms using HRR profilesand 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


4/167

iv

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.


5/167

v

CONTENTS

1: Introduction 1

1.1 ATR/Target Detection review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1.1 A review of ATR/Target detection . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1.2 Moving Target Indicator (MTI) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1.3 Synthetic Aperture Radar (SAR) . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1.4 High Range Resolution Radar (HRR) . . . . . . . . . . . . . . . . . . . . . . .

1

1

2

4

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2: Robust HRR Radar Target Identification by Hybridization of HMM and

Eigen Template based Matched Filtering

19

2.1ETMF Approach of training and classification . . . . . . . . . . . . . . . . . . . . . .

2.1.1 HRR Data Generation and Preprocessing . . . . . . . . . . . . . . . . . . . . . .

2.1.2: Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

20

22


6/167

vi

2.1.3: Alignment of HRR Profiles in Range . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.4: Eigen-analysis of HRR data for training . . . . . . . . . . . . . . . . . . . . . .

2.1.5: Unknown Target Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.6:Modified Normalization and Centroid Alignment . . . . . . . . . . . . . . .

22

22

25

26

2.2:HMM approach of training and classification . . . . . . . . . . . . . . . . . . . . . . .

2.2.1: Discrete Hidden Markov Model Introduction . . . . . . . . . . . . . . . . . .

2.2.1.1: Elements of HMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1.2: Three Basic Problems for HMM . . . . . . . . . . . . . . . . . . . . . . .

2.2.1.3: Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1.4: Optimal State Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.1.5: Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2: HMM Operation steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.1: Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.2: Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.3: HMM Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.3.1: Model Optimum Parameter estimation . . . . . . . . . . . .

2.2.2.3.2: Optimum state sequence estimation . . . . . . . . . . . . . .

2.2.2.4: HMM Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.4.1: The Forward Procedure . . . . . . . . . . . . . . . . . . . . . . . .

2.2.2.4.2: The Backward Procedure . . . . . . . . . . . . . . . . . . . . . .

30

31

32

34

34

36

36

36

36

37

39

40

45

47

48

52

2.3: Approach of Combination between ETMF and HMM . . . . . . . . . . . . . . . .

2.3.1: Motivation for Hybrid approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.2: Proposed Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

53

54


7/167

vii

2.3.2.1: Necessity of developing modified hybridization in ETMF ATR

2.3.2.2: Number of Subset Model selection and Weight calculation . . .

2.3.2.2.1: Subset Model Selection . . . . . . . . . . . . . . . . . . . . . . . .

2.3.2.2.2: Weight determination . . . . . . . . . . . . . . . . . . . . . . . . .

56

58

58

61

2.4: Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.1: Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.2: ETMF Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.2.1: Formation of Template Profiles . . . . . . . . . . . . . . . . . . . . . . . .

2.4.2.2: Classification using Matched Filter Technique . . . . . . . . . . . .

2.4.3: HMM Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.3.1: Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.3.2: Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.3.3: Training and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.4: Single Look Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.4.1: Forced Decision Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.4.2: Classification in Unknown Target Scenario . . . . . . . . . . . . . . .

2.4.4.3: Computational Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4.5: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

64

64

64

65

65

65

65

66

66

67

73

86

87

3:Time Recursive Multiple Hypothesis Testing 88

3.1: Theory Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.2: Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1: ETMF classifier Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . .

91

92


8/167

viii

3.2.1.1: Description of MSTAR Data . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1.2: Multilook Performance Results . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2: Hybrid Classifier Simulation results . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.3: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

93

95

98

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 . . . . . . . . . . . . . . . . . . . . . .

4.5.1: Energy Normalized SVD (EN-SVD) . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.1.1: Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.1.2: EN-SVD Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.1.3: EN-SVD Testing Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.2: Condition-Statistic SVD (CS-SVD) . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.3: Terrain-Filtered SVD (TF-SVD) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.3.1: Motivation and Kernel formation . . . . . . . . . . . . . . . . . . . . . . . .

4.5.3.2: Implementation steps of TF-SVD . . . . . . . . . . . . . . . . . . . . . . .

4.5.4: Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.4.1: UWB SAR simulated image specification . . . . . . . . . . . . . . . .

4.5.4.2: Performance Comparison of Target Detection algorithms . . . .

4.5.4.2.1: Performance Comparison in Offline training mode . .

108

108

108

110

113

114

115

115

118

119

120

122

122


9/167

ix

4.5.4.2.2: Performance Comparison in Self-Training mode . . . .

4.5.4.3: Performance Comparison of various techniques . . . . . . . . . . .

4.5.4.4: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

132

135

5: Summary and Future work 137

5.1: Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.1.1: Hybrid ATR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.1.2: Time Recursive Sequential ATR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.1.3: SAR target detection algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.2: Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Bibliography 141


10/167

x

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

boxes of different lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

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

V2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.10 Flow diagram for LBG clustering algorithm . . . . . . . . . . . . . . . . . . . . . 38

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

time t+1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

2.12 Baum-Welch learning algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44


11/167

xi

2.13 Block Diagram of a Designed HMM recognizer. . . . . . . . . . . . . . . . . 47

2.14 Illustration of the sequence of operations required for the computation

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

number of HMM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

2.18 This figure is used to determine the most effective W1/ W2 so that the

combined ETMF+HMM recognition rate is the highest . . . . . . . . . . . .

62

2.19 Bar plot representation of ETMF, HMM and Hybrid classifier

performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

2.20 ROC curves for Probability of declaration vs Conditional Probability

of Correct Classification (Single profile) . . . . . . . . . . . . . . . . . . . . . . . .

78

2.21 ROC curves for Probability of False Alarm vs Probability of

Declaration (Single profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78


of Correct Classification (3 profile average) . . . . . . . . . . . . . . . . . . . . .

80


Declaration (3 profile average) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80


of Correct Classification (5 profile average) . . . . . . . . . . . . . . . . . . . . .

81


Declaration (5 profile average) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81


12/167

xii

2.26 ROC curves for Probability of Declaration vs Conditional Probability

of Correct Identification (Combined result) . . . . . . . . . . . . . . . . . . . . . .

82


declaration (Combined result) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

2.28 ROC curves for Probability of False Alarm vs Conditional Probability

of Correct Classification (Combined result) . . . . . . . . . . . . . . . . . . . . .

83

3.1 Block diagram for time recursive multiple hypothesis Combiner . . . . . 91

3.2 ROC curves for Probability of detection vs Conditional Probability of

Correct Classification (time recursive ETMF) . . . . . . . . . . . . . . . . . . . .

93


declaration (time recursive ETMF) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94


declaration (time recursive hybrid) . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

3.5 ROC curves for Probability of Declaration vs Conditional Probability

of Correct Identification (time recursive hybrid) . . . . . . . . . . . . . . . . . .

96

3.6 ROC curves for Probability of False Alarm vs Conditional Probability

of Correct Identification (time recursive hybrid) . . . . . . . . . . . . . . . . . .

96

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


13/167

xiii

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

operation in TF-SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

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

offline training-real time testing mode . . . . . . . . . . . . . . . . . . . . . . . . . .

127

4.13 Performance comparison of EN-SVD, CS-SVD and TF-SVD shown

in logarithmic scale in offline training-real time testing mode . . . . . . .

128

4.14 Performance comparison of EN-SVD, CS-SVD and TF-SVD in self-

train mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

130

4.15 Performance comparison of EN-SVD, CS-SVD and TF-SVD in self-

train mode (logarithmic scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132

4.16 ROCPerformance comparison of various techniques . . . . . . . . . . . . . . 133

4.17 ROCPerformance comparison of various techniques (logarithmic

scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

134


14/167

xiv

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

testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

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

testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

XII Evaluation parameter computation from the confusion matrix . . . . 74

XIII Confusion matrix (Unknown rejection threshold about 0.6) for

ETMF based classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

XIV Confusion matrix (Unknown rejection threshold about 0.6) for

Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76


15/167

xv

XV Confusion matrix (Unknown rejection threshold about 0.6) for


76

XVI Confusion matrix (Unknown rejection threshold about 0.6) for

Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

XVII Confusion matrix (Unknown rejection threshold about 0.6) for


77

XVIII Confusion matrix (Unknown rejection threshold about 0.6) for

Hybrid classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

XIX Conditional Probability of Correct Classification of Hybrid and

ETMF classifiers at Pd = 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

XX Probability of Declaration of Hybrid and ETMF classifiers at Pfa =

0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

XXI Conditional Probability of Correct Classification of Hybrid and

ETMF classifiers at Pfa = 0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

XXII Improvement of Probability of Declaration of Hybrid classifiers

due to time recursive multilook approaches at Pfa = 0.4 . . . . . . . . .

97

XXIII Improvement of Conditional Probability of Correct Classification

of Hybrid classifiers due to time recursive multilook approaches at

Pd = 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

XXIV Improvement of Conditional Probability of Correct Classification

of Hybrid classifiers due to time recursive multilook approaches at

Pfa = 0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97


16/167

xvi

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.


17/167

1

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


18/167

2

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


19/167

3

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]. MTIs are operated with either fixed based or a moving

platform such as an aircraft or a satellite. Considering detection of low flying aircrafts,

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.


20/167


21/167

5

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/(2(d/dt)), where =

4R/. 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.


22/167

6

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 Cross-

Range resolution is limited by the migration of scatterers into neighboring resolution

cells.


23/167

7

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.

Figure 1.1: Side looking radar system geometry


24/167

8

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. SAR-

detection/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.


25/167

9

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. Bottcheret 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


26/167

10

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 [53-

54]. 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


27/167

11

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


28/167

12

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.

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. Also there is considerable saving in front end

processing in HRR profile generation which require 1-D FFT operation as opposed to

SARs 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.


29/167

13

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


30/167

14

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 sub-

targets. 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 [59-

60]. But this thesis concentrates on recognition of stationary targets using the MSTAR

data.


31/167

15

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 ultra-

wideband (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 ultra-

wideband 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 off-

line 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:


32/167

16

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


33/167

17

approach, a number of categories of algorithms are investigated that implement self-

training 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.


34/167

18

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.


35/167

19

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


36/167

20

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


37/167

21

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 ( j )) in each Range gate would be

i

2N j4 R

j i

i 1

Y( ) e

=

(2.1)

Where i is the RCS of elemental scatterers in Range gate, Ri is the Range and N is the

number of scatterers in a Range gate.

IFFT (r2+x

2)

1/2Complex phase

history (CPH) Complex

HRR

SVDEigen

Templates

Detected

HRR profiles

Fig. 2.1:Eigen-Template Generation from detected HRR profiles


38/167

22

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 NXM:Detected HRR Profile Matrix, N = No. of Range profiles and M = No.of Angular looks


39/167

23

M

SVD T T

i i i

i 1=

= Y U V u v (2.2)

where,

Range-Space (Left) Eigen Vectors : (Use as Features)

T= EV[ ] = [ ...... ]1 nU YY u u NXM

(2.3)

Angle-Space(Right) Eigen Vectors : (Discard)

EV[ ] [ ]= =T

1 mV Y Y v ....v NXM

(2.4)

Singular Values :

11 MM = Diagonal[ ...... ]NXM (2.5)

Range and Angle sub-spaces are decoupled via SVD.

0 5 10 15 20 25 30 350

1

2

3

4

5

6

Number of Eigen Values

Magnitude

Eigen Value Distribution

Fig. 2.2: Distribution of Singular values for MSTAR target T72, 1000 sector


40/167

24

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 is diagonal

containing M (N>M is assumed here) singular values in decreasing order,

11 22 MM... , where 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 (11

) 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 that1u , the left-

eigenvector corresponding to the largest (or dominant) singular value ( 1 ) 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.


41/167

25

2.1.5: Unknown Target Classification

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 ( im ) 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

Template

|||Test Profile (shift = -8)

||

Test Profile (shift = 0)

||Test Profile (shift =+ 8)

Fig. 2.3: Implementation of the Correlation Classifier


42/167

26

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 pre-

aligned 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


43/167

27

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 MFs 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.

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 doesnt make any

sense to normalize over entire lengths of the template or test, because the correlation is

OBSERVATION PROFILEA

Template Profile

Fig. 2.4: Observation and Template Profiles are shown in shaded and blank boxes of different lengths


44/167

28

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.

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.

Fig. 2.5: Shift = -8 of Centroid

Overlap region to be normalized


45/167

29

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


Fig. 2.6: Shift = 0 aligned of Centroid


Fig. 2.7: Shift = +8 of the Centroid


46/167

30

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)

Code Book

HRR profiles

(Test data)

Training Model

(HMM)

Testing Target

Classification

Fig. 2.8. Simplified Block diagram of target recognition using HMM


47/167

31

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, HMMs 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 HMMs, 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.


48/167

32

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 = , 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

{ }1 2 3 NS = s ,s ,s ,...s , and the state at time t as qt.


49/167

33

M: the number of distinct observable symbols per state or the size of the codebook.

We denote the individual symbols as { }1 2 3 MV = v , v , v ,..., v , 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:

{ } ( )ij ij t j t -1 i= a where a = prob q = s | q = s 1 i, j N A (2.8)

And

N

ij ij ij

j 1

a 0, a 1 ,1 a N=

= (2.9)

B:NxMmatrixwhich specifies the observation symbol probability distribution in the

state sj:

{ }j j k t jb (k) where b (k) prob(v t | q s ), 1 j N, 1 k M= = = = B (2.10)

And

M

j j

k 1

b (k) 0, b (k) 1 , 1 j N=

= (2.11)

: N-element vector indicating the initial state probability distribution:

{ }i i 1 i, where prob(q s ), 1 i N= = = (2.12)

The complete parameter set of HMM requires the specification of two modelparameters (N and M), the specification of the observation symbols, and the specification


50/167

34

of the three probability matrices A, B and . The compact but convenient notation is usedto represent the parameter set of HMM model.

( ), ,= A B (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 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

1 2 TO O ...O=O , and a HMM model ( ), ,= A B , compute ( )P O , 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.


51/167

35

( ) ( ) ( )all Q

P | P | P | ,= O Q O Q (2.14)

Where Q is the state sequence: 1 2 Tq q q=Q L and q1 is the initial state. The first factor in

Equation (2.14) can be re-written by applying the two Markov assumptions:

( )1 1 2 2 3 T 1 T

T

t t 1 q q q q q q q

t 1

P | P(q | q ) a a a

=

= = Q L (2.15)

The second factor in Equation (2.14) can be re-written by applying the output-

independence assumption:

( ) ( ) ( ) ( )1 2 Tq 1 q 2 q TP | , b O b O b O= O Q L (2.16)

Substituting Equation (2.16) and (2.15) into (2.14), we have:

( ) ( ) ( )allQ

P | P | P | ,= O Q O Q (2.17)

1 1 1 2 2 T 1 T T

1 2 T

q q 1 q q q 2 q q q T

q ,q ,...q

b (O )a b (O )...a b (O )

= (2.18)

From Equation (2.18) we can directly calculate the ( )P O 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 recursively.


52/167

36

2.2.1.4: Optimal State Sequence

Given a model and a sequence of observations 1 2 TO O ...O=O , one problem that needs

to be addressed is the estimate of the best state sequence 1 2 Tq q ...q=Q (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 , which is equivalent to maximizing ( )P ,Q O .

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 such that its likelihood function P( | )O is locallymaximized.

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


53/167

37

number of samples, framing is pretty useful to duplicate the information contained in a

single profile and learning the HMM. Framing is done on HRR profiles used both for

training and testing.

2.2.2.2:Clustering

The next specific step is to make target and aspect specific Vector Quantization (VQ)

codebook. The importance of codebook is to cluster the data in feature space. A

commonly used LBG algorithm [61] for clustering a set of L frame vectors into a set of C

codebook vectors was formally implemented by the following recursive algorithm:

1) Design a 1-vector codebook; this is the centroid of the entire set of training vectors

(hence, no iteration is required here).

2) Double the size of the codebook by splitting each current codebookyn according to the

rule:

n ny y (1 )+ = + (2.19)

n ny y (1 ) = (2.20)

Where n varies from 1 to the current size of the codebook, and is a splitting parameter

or learning parameter (we choose = 0.01).

3) Nearest-Neighbor Search: for each training vector, find the codeword in the current

codebook that is closest (in terms of similarity measurement, here we have taken as

Euclidean distance as similarity measure), and assigns that vector to the corresponding

cell (associated with the closest codeword).

4) Centroid Update: update the codeword in each cell using the centroid of the training

vectors assigned to that cell.


54/167

38

Iteration 1: repeat steps 3 and 4 until the average distance falls below a preset threshold.

Iteration 2: repeat steps 2, 3 and 4 until a codebook size of C is designed.

Figure 2.10 shows, in a flow diagram, the detailed steps of the LBG algorithm.

Cluster vectors is the nearest-neighbor search procedure that assigns each training

vector to a cluster associated with the closest codeword. Find centroids is the centroid

update procedure. Compute D (distortion) sums the distances of all training vectors in

the nearest-neighbor search so as to determine whether the procedure has converged.

Findcentroid

Split eachcentroid

Clustervectors

Findcentroids

Compute D

(distortion)

improved target recognition (book)

Documents