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E-raamat: Radar Data Processing with Applications [Wiley Online]

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  • Formaat: 560 pages
  • Sari: IEEE Press
  • Ilmumisaeg: 28-Oct-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118956877
  • ISBN-13: 9781118956878
Teised raamatud teemal:
  • Wiley Online
  • Hind: 169,17 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Radar Data Processing with ApplicationsSuurem pilt
  • Formaat: 560 pages
  • Sari: IEEE Press
  • Ilmumisaeg: 28-Oct-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118956877
  • ISBN-13: 9781118956878
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118956878
Radar Data Processing with Applications Radar Data Processing with Applications

He You, Xiu Jianjuan, Guan Xin, Naval Aeronautical and Astronautical University, China

A summary of thirty years worth of research, this book is a systematic introduction to the theory, development, and latest research results of radar data processing technology. Highlights of the book include sections on data pre-processing technology, track initiation, and data association. Readers are also introduced to maneuvering target tracking, multiple target tracking termination, and track management theory. In order to improve data analysis, the authors have also included group tracking registration algorithms and a performance evaluation of radar data processing.





Presents both classical theory and development methods of radar data processing Provides state-of-the-art research results, including data processing for modern radars and tracking performance evaluation theory Includes coverage of performance evaluation, registration algorithm for radar networks, data processing of passive radar, pulse Doppler radar, and phased array radar Features applications for those engaged in information engineering, radar engineering, electronic countermeasures, infrared techniques, sonar techniques, and military command

Radar Data Processing with Applications is a handy guide for engineers and industry professionals specializing in the development of radar equipment and data processing. It is also intended as a reference text for electrical engineering graduate students and researchers specializing in signal processing and radars.
About the Authors xiv
Preface xvi
1 Introduction 1(19)
1.1 Aim and Significance of Radar Data Processing
1(1)
1.2 Basic Concepts in Radar Data Processing
2(7)
1.2.1 Measurements
2(1)
1.2.2 Measurement Preprocessing
2(2)
1.2.3 Data Association
4(1)
1.2.4 Wave Gate
4(1)
1.2.5 Track Initiation and Termination
5(1)
1.2.6 Tracking
5(2)
1.2.7 Track
7(2)
1.3 Design Requirements and Main Technical Indexes of Radar Data Processors
9(3)
1.3.1 Basic Tasks of Data Processors
9(1)
1.3.2 The Engineering Design of Data Processors
9(2)
1.3.3 The Main Technical Indexes of Data Processors
11(1)
1.3.4 The Evaluation of Data Processors
11(1)
1.4 History and Present Situation of Research in Radar Data Processing Technology
12(2)
1.5 Scope and Outline of the Book
14(6)
2 Parameter Estimation 20(14)
2.1 Introduction
20(1)
2.2 The Concept of Parameter Estimation
20(3)
2.3 Four Basic Parameter Estimation Techniques
23(3)
2.3.1 Maximum A Posteriori Estimator
23(1)
2.3.2 Maximum Likelihood Estimator
24(1)
2.3.3 Minimum Mean Square Error Estimator
24(2)
2.3.4 Least Squares Estimator
26(1)
2.4 Properties of Estimators
26(2)
2.4.1 Unbiasedness
26(1)
2.4.2 The Variance of an Estimator
26(1)
2.4.3 Consistent Estimators
26(1)
2.4.4 Efficient Estimators
27(1)
2.5 Parameter Estimation of Static Vectors
28(5)
2.5.1 Least Squares Estimator
28(2)
2.5.2 Minimum Mean Square Error Estimator
30(2)
2.5.3 Linear Minimum Mean Square Error Estimator
32(1)
2.6 Summary
33(1)
3 Linear Filtering Approaches 34(19)
3.1 Introduction
34(1)
3.2 Kalman Filter
34(14)
3.2.1 System Model
35(6)
3.2.2 Filtering Model
41(3)
3.2.3 Initialization of Kalman Filters
44(4)
3.3 Steady-State Kalman Filter
48(4)
3.3.1 Mathematical Definition and Judgment Methods for Filter Stability
49(1)
3.3.2 Controllability and Observability of Random Linear System
49(1)
3.3.3 Steady-State Kalman Filter
50(2)
3.4 Summary
52(1)
4 Nonlinear Filtering Approaches 53(19)
4.1 Introduction
53(1)
4.2 Extended Kalman Filter
53(5)
4.2.1 Filter Model
54(4)
4.2.2 Some Problems in the Application of Extended Kalman Filters
58(1)
4.3 Unscented Kalman Filter
58(7)
4.3.1 Unscented Transformation
59(1)
4.3.2 Filtering Model
60(1)
4.3.3 Simulation Analysis
61(4)
4.4 Particle Filter
65(7)
4.4.1 Filtering Model
65(2)
4.4.2 Examples of the Application of EKF, UKF, and PF
67(4)
4.5 Summary
71(1)
5 Measurement Preprocessing Techniques 72(23)
5.1 Introduction
72(1)
5.2 Time Registration
72(3)
5.2.1 Interpolation/Extrapolation Method Using Velocity
73(1)
5.2.2 The Lagrange Interpolation Algorithm
74(1)
5.2.3 Least-Squares Curve-Fitting Algorithm
74(1)
5.3 Space Registration
75(13)
5.3.1 Coordinates
75(5)
5.3.2 Coordinate Transformation
80(3)
5.3.3 Transformation of Several Common Coordinate Systems
83(4)
5.3.4 Selection of Tracking Coordinate Systems and Filtering State Variables
87(1)
5.4 Radar Error Calibration Techniques
88(1)
5.5 Data Compression Techniques
89(4)
5.5.1 Data Compression in Monostatic Radar
89(2)
5.5.2 Data Compression in Multistatic Radar
91(2)
5.6 Summary
93(2)
6 Track Initiation in Multi-target Tracking 95(23)
6.1 Introduction
95(1)
6.2 The Shape and Size of Track Initiation Gates
96(4)
6.2.1 The Annular Gate
96(1)
6.2.2 The Elliptic/Ellipsoidal Gate
97(2)
6.2.3 The Rectangular Gate
99(1)
6.2.4 The Sector Gate
99(1)
6.3 Track Initiation Algorithms
100(9)
6.3.1 Logic-Based Method
101(1)
6.3.2 Modified Logic-Based Method
102(1)
6.3.3 Hough Transform-Based Method
103(3)
6.3.4 Modified Hough Transform-Based Method
106(1)
6.3.5 Hough Transform and Logic-Based Method
107(1)
6.3.6 Formation Target Method Based on Clustering and Hough Transform
108(1)
6.4 Comparison and Analysis of Track Initiation Algorithms
109(7)
6.5 Discussion of Some Issues in Track Initiation
116(1)
6.5.1 Main Indicators of Track Initiation Performance
116(1)
6.5.2 Demonstration of Track Initiation Scan Times
116(1)
6.6 Summary
117(1)
7 Maximum Likelihood Class Multi-target Data Association Methods 118(20)
7.1 Introduction
118(1)
7.2 Track-Splitting Algorithm
118(5)
7.2.1 Calculation of Likelihood Functions
119(1)
7.2.2 Threshold Setting
120(1)
7.2.3 Modified Likelihood Function
121(1)
7.2.4 Characteristics of Track-Splitting Algorithm
122(1)
7.3 Joint Maximum Likelihood Algorithm
123(3)
7.3.1 Establishment of Feasible Partitions
123(2)
7.3.2 Recursive Joint Maximum Likelihood Algorithm
125(1)
7.4 0-1 Integer Programming Algorithm
126(4)
7.4.1 Calculation of the Logarithm Likelihood Ratio
126(2)
7.4.2 0-1 Linear Integer Programming Algorithm
128(1)
7.4.3 Recursive 0-1 Integer Programming Algorithm
129(1)
7.4.4 Application of 0-1 Integer Programming Algorithm
130(1)
7.5 Generalized Correlation Algorithm
130(7)
7.5.1 Establishing the Score Function
130(3)
7.5.2 Application of the Generalized Correlation Algorithm
133(4)
7.6 Summary
137(1)
8 Bayesian Multi-target Data Association Approach 138(31)
8.1 Introduction
138(1)
8.2 Nearest-Neighbor Algorithm
138(3)
8.2.1 Nearest-Neighbor Standard Filter
138(1)
8.2.2 Probabilistic Nearest-Neighbor Filter Algorithm
139(2)
8.3 Probabilistic Data Association Algorithm
141(11)
8.3.1 State Update and Covariance Update
141(3)
8.3.2 Calculation of the Association Probability
144(2)
8.3.3 Modified PDAF Algorithm
146(1)
8.3.4 Performance Analysis
147(5)
8.4 Integrated Probabilistic Data Association Algorithm
152(2)
8.4.1 Judgment of Track Existence
152(2)
8.4.2 Data Association
154(1)
8.5 Joint Probabilistic Data Association Algorithm
154(13)
8.5.1 Basic Models of JPDA
155(5)
8.5.2 Calculation of the Probability of Joint Events
160(2)
8.5.3 Calculation of the State Estimation Covariance
162(2)
8.5.4 Simplified JPDA Model
164(1)
8.5.5 Performance Analysis
165(2)
8.6 Summary
167(2)
9 Tracking Maneuvering Targets 169(34)
9.1 Introduction
169(1)
9.2 Tracking Algorithm with Maneuver Detection
170(4)
9.2.1 White Noise Model with Adjustable Level
171(1)
9.2.2 Variable-Dimension Filtering Approach
172(2)
9.3 Adaptive Tracking Algorithm
174(15)
9.3.1 Modified-Input Estimation Algorithm
174(2)
9.3.2 Singer Model Tracking Algorithm
176(4)
9.3.3 Current Statistical Model Algorithm
180(2)
9.3.4 Jerk Model Tracking Algorithm
182(2)
9.3.5 Multiple Model Algorithm
184(2)
9.3.6 Interacting Multiple Model Algorithm
186(3)
9.4 Performance Comparison of Maneuvering Target Tracking Algorithms
189(12)
9.4.1 Simulation Environment and Parameter Setting
189(2)
9.4.2 Simulation Results and Analysis
191(10)
9.5 Summary
201(2)
10 Group Target Tracking 203(47)
10.1 Introduction
203(1)
10.2 Basic Methods for Track Initiation of the Group Target
204(10)
10.2.1 Group Definition
204(1)
10.2.2 Group Segmentation
205(3)
10.2.3 Group Correlation
208(1)
10.2.4 Group Velocity Estimation
209(5)
10.3 The Gray Fine Track Initiation Algorithm for Group Targets
214(19)
10.3.1 Gray Fine Association of Targets within the Group Based on the Relative Position Vector of the Measurement
215(5)
10.3.2 Confirmation of the Tracks within a Group
220(1)
10.3.3 Establishment of State Matrixes for Group Targets
221(1)
10.3.4 Simulation Verification and Analysis of the Algorithm
221(10)
10.3.5 Discussion
231(2)
10.4 Centroid Group Tracking
233(5)
10.4.1 Initiation, Confirmation, and Cancellation of Group Tracks
234(1)
10.4.2 Track Updating
234(3)
10.4.3 Other Questions
237(1)
10.5 Formation Group Tracking
238(2)
10.5.1 Overview of Formation Group Tracking
238(1)
10.5.2 Logic Description of Formation Group Tracking
238(2)
10.6 Performance Analysis of Tracking Algorithms for Group Targets
240(6)
10.6.1 Simulation Environment
240(1)
10.6.2 Simulation Results
240(1)
10.6.3 Simulation Analysis
240(6)
10.7 Summary
246(4)
11 Multi-target Track Termination Theory and Track Management 250(26)
11.1 Introduction
250(1)
11.2 Multi-target Track Termination Theory
250(8)
11.2.1 Sequential Probability Ratio Test Algorithm
250(2)
11.2.2 Tracking Gate Method
252(1)
11.2.3 Cost Function Method
253(1)
11.2.4 Bayesian Algorithm
254(1)
11.2.5 All-Neighbor Bayesian Algorithm
255(1)
11.2.6 Performance Analysis of Several Algorithms
256(2)
11.3 Track Management
258(17)
11.3.1 Track Batch Management
258(8)
11.3.2 Track Quality Management
266(7)
11.3.3 Track File Management in the Information Fusion System
273(2)
11.4 Summary
275(1)
12 Passive Radar Data Processing 276(28)
12.1 Introduction
276(1)
12.2 Advantages of Passive Radars
276(2)
12.3 Passive Radar Spatial Data Association
278(11)
12.3.1 Phase Changing Rate Method
278(5)
12.3.2 Doppler Changing Rate and Azimuth Joint Location
283(2)
12.3.3 Doppler Changing Rate and Azimuth, Elevation Joint Location
285(1)
12.3.4 Multiple-Model Method
286(3)
12.4 Optimal Deployment of Direction-Finding Location
289(10)
12.4.1 Area of the Position Concentration Ellipse
289(3)
12.4.2 Derivation of the Conditional Extremum Based on the Lagrange Multiplier Method
292(5)
12.4.3 Optimal Deployment by the Criterion that the Position Concentration Ellipse Area is Minimum
297(2)
12.5 Passive Location Based on TDOA Measurements
299(4)
12.5.1 Location Model
299(1)
12.5.2 Two-Dimensional Condition
299(2)
12.5.3 Three-Dimensional Condition
301(2)
12.6 Summary
303(1)
13 Pulse Doppler Radar Data Processing 304(28)
13.1 Introduction
304(1)
13.2 Overview of PD Radar Systems
304(3)
13.2.1 Characteristics of PD Radar
304(1)
13.2.2 PD Radar Tracking System
305(2)
13.3 Typical Algorithms of PD Radar Tracking
307(14)
13.3.1 Optimal Range-Velocity Mutual Coupling Tracking
309(3)
13.3.2 Multi-target Tracking
312(1)
13.3.3 Target Tracking with Doppler Measurements
312(9)
13.4 Performance Analysis on PD Radar Tracking Algorithms
321(10)
13.4.1 Simulation Environments and Parameter Settings
321(1)
13.4.2 Simulation Results and Analysis
322(9)
13.5 Summary
331(1)
14 Phased Array Radar Data Processing 332(30)
14.1 Introduction
332(1)
14.2 Characteristics and Major Indexes
333(1)
14.2.1 Characteristics
333(1)
14.2.2 Major Indexes
334(1)
14.3 Structure and Working Procedure
334(2)
14.3.1 Structure
334(1)
14.3.2 Working Procedure
335(1)
14.4 Data Processing
336(19)
14.4.1 Single-Target-in-Clutter Tracking Algorithms
337(6)
14.4.2 Multi-target-in-Clutter Tracking Algorithm
343(2)
14.4.3 Adaptive Sampling Period Algorithm
345(4)
14.4.4 Real-Time Task Scheduling Strategy
349(6)
14.5 Performance Analysis of the Adaptive Sampling Period Algorithm
355(6)
14.5.1 Simulation Environment and Parameter Settings
355(1)
14.5.2 Simulation Results and Analysis
356(4)
14.5.3 Comparison and Discussion
360(1)
14.6 Summary
361(1)
15 Radar Network Error Registration Algorithm 362(43)
15.1 Introduction
362(1)
15.2 The Composition and Influence of Systematic Errors
362(4)
15.2.1 The Composition of Systematic Errors
362(1)
15.2.2 The Influence of Systematic Errors
363(3)
15.3 Fixed Radar Registration Algorithm
366(14)
15.3.1 Radar Registration Algorithm Based on Cooperative Targets
366(2)
15.3.2 RTQC Algorithm
368(2)
15.3.3 LS Algorithm
370(1)
15.3.4 GLS Algorithm
371(2)
15.3.5 GLS Algorithm in ECEF Coordinate System
373(4)
15.3.6 Simulation Analysis
377(3)
15.4 Mobile Radar Registration Algorithm
380(22)
15.4.1 Modeling Method of Mobile Radar Systems
380(6)
15.4.2 Mobile Radar Registration Algorithm Based on Cooperative Targets
386(4)
15.4.3 Mobile Radar Maximum Likelihood Registration Algorithm
390(7)
15.4.4 ASR Algorithm
397(1)
15.4.5 Simulation Analysis
398(4)
15.5 Summary
402(3)
16 Radar Network Data Processing 405(22)
16.1 Introduction
405(1)
16.2 Performance Evaluation Indexes of Radar Networks
406(2)
16.2.1 Coverage Performance Indexes
406(1)
16.2.2 Target Capacity
407(1)
16.2.3 Anti jamming Ability
407(1)
16.3 Data Processing of Monostatic Radar Networks
408(5)
16.3.1 The Process of Data Processing of the Monostatic Radar Network
408(2)
16.3.2 State Estimation of Monostatic Radar Networks
410(3)
16.4 Data Processing of Bistatic Radar Networks
413(7)
16.4.1 Basic Location Relation
413(3)
16.4.2 Combined Estimation
416(1)
16.4.3 An Analysis of the Feasibility of Combinational Estimation
417(3)
16.5 Data Processing of Multistatic Radar Networks
420(3)
16.5.1 Tracking Principle of Multistatic Radar Systems
421(1)
16.5.2 Observation Equation of Multistatic Radar Network Systems
422(1)
16.5.3 The Generic Data Processing Process of Multistatic Tracking Systems
422(1)
16.6 Track Association
423(3)
16.7 Summary
426(1)
17 Evaluation of Radar Data Processing Performance 427(14)
17.1 Introduction
427(1)
17.2 Basic Terms
428(1)
17.3 Data Association Performance Evaluation
429(3)
17.3.1 Average Track Initiation Time
429(1)
17.3.2 Accumulative Number of Track Interruptions
430(1)
17.3.3 Track Ambiguity
431(1)
17.3.4 Accumulative Number of Track Switches
432(1)
17.4 Performance Evaluation of Tracking
432(4)
17.4.1 Track Accuracy
433(1)
17.4.2 Maneuvering Target Tracking Capability
434(1)
17.4.3 False Track Ratio
434(1)
17.4.4 Divergence
435(1)
17.5 Evaluation of the Data Fusion Performance of Radar Networks
436(2)
17.5.1 Track Capacity
436(1)
17.5.2 Detection Probability of Radar Networks
436(1)
17.5.3 Response Time
437(1)
17.6 Methods of Evaluating Radar Data Processing Algorithms
438(2)
17.6.1 Monte Carlo Method
438(1)
17.6.2 Analytic Method
438(1)
17.6.3 Semi-physical Simulation Method
439(1)
17.6.4 Test Validation Method
440(1)
17.7 Summary
440(1)
18 Radar Data Processing Simulation Technology 441(23)
18.1 Introduction
441(1)
18.2 Basis of System Simulation Technology
442(7)
18.2.1 Basic Concept of System Simulation Technology
442(2)
18.2.2 Digital Simulation of Stochastic Noise
444(5)
18.3 Simulation of Radar Data Processing Algorithms
449(8)
18.3.1 Simulation of Target Motion Models
449(3)
18.3.2 Simulation of the Observation Process
452(1)
18.3.3 Tracking Filtering and Track Management
453(4)
18.4 Simulation Examples of Algorithms
457(6)
18.5 Summary
463(1)
19 Practical Application of Radar Data Processing 464(35)
19.1 Introduction
464(1)
19.2 Application in ATC Systems
464(10)
19.2.1 Application, Components, and Requirement
464(2)
19.2.2 Radar Data Processing Structure
466(1)
19.2.3 ATC Application
467(7)
19.3 Application in Shipboard Navigation Radar
474(2)
19.4 Application in Shipboard Radar Clutter Suppression
476(4)
19.4.1 Principle of Clutter Suppression in Data Processing
476(1)
19.4.2 Clutter Suppression Method through Shipboard Radar Data Processing
477(3)
19.5 Application in Ground-Based Radar
480(2)
19.5.1 Principle of Data Acquisition
480(1)
19.5.2 Data Processing Procedure
481(1)
19.6 Applications in Shipboard Monitoring System
482(2)
19.6.1 Application, Components, and Requirement
482(1)
19.6.2 Structure of the Marine Control System
483(1)
19.7 Application in the Fleet Air Defense System
484(2)
19.7.1 Components and Function of the Aegis Fleet Air Defense System
484(1)
19.7.2 Main Performance Indexes
485(1)
19.8 Applications in AEW Radar
486(6)
19.8.1 Features, Components, and Tasks
486(1)
19.8.2 Data Processing Technology
487(2)
19.8.3 Typical Working Mode
489(3)
19.9 Application in Air Warning Radar Network
492(3)
19.9.1 Structure of Radar Network Data Processing
492(1)
19.9.2 Key Technologies of Radar Network Data Processing
493(2)
19.10 Application in Phased Array Radar
495(3)
19.10.1 Functional Features
495(1)
19.10.2 Data Processing Procedure
495(1)
19.10.3 Test Examples
496(2)
19.11 Summary
498(1)
20 Review, Suggestions, and Outlook 499(9)
20.1 Introduction
499(1)
20.2 Review of Research Achievements
499(3)
20.2.1 The Basis of State Estimation
499(1)
20.2.2 Measurement Preprocessing Technology
500(1)
20.2.3 Track Initiation in Multi-target Tracking
500(1)
20.2.4 Multi-target Data Association Method
500(1)
20.2.5 Maneuvering Target and Group Tracking
500(1)
20.2.6 Multi-target Tracking Termination Theory and Track Management
501(1)
20.2.7 System Error Registration Issue
501(1)
20.2.8 Performance Evaluation of Radar Data Processors
501(1)
20.2.9 Simulation Technology of Radar Data Processing
501(1)
20.2.10 Applications of Radar Data Processing Techniques
502(1)
20.3 Issues and Suggestions
502(3)
20.3.1 The Application of Data Processing Technology in Other Sensors
502(1)
20.3.2 Track Initiation in Passive Sensor Tracking
502(1)
20.3.3 Non-Gaussian Noise
503(1)
20.3.4 Data Processing in Non-standard and Nonlinear Systems
503(1)
20.3.5 Data Processing in Multi-radar Networks
503(1)
20.3.6 Joint Optimization of Multi-target Tracking and Track Association
503(1)
20.3.7 Comprehensive Utilization of Target Features and Attributes in Multi-radar Tracking
504(1)
20.3.8 Comprehensive Optimization of Multi-radar Information Fusion Systems
504(1)
20.3.9 Tracking Multi-targets in Complex Electromagnetic Waves and Dense Clutter
504(1)
20.4 Outlook for Research Direction
505(3)
20.4.1 Information Fusion and Control Integration Technology of Multi-radar Networks
505(1)
20.4.2 Joint Optimization of Target Tracking and Identification
505(1)
20.4.3 Integration Technology of Search, Tracking, Guidance, and Command
505(1)
20.4.4 Multi-radar Resource Allocation and Management Technology
505(1)
20.4.5 Database and Knowledge Base Technology in Radar Data Processing
506(1)
20.4.6 Engineering Realization of Advanced Radar Data Processing Algorithms
506(1)
20.4.7 High-Speed Calculation and Parallel Processing Technology
506(1)
20.4.8 Establishment of System Performance Evaluation Methods and Test Platforms
506(1)
20.4.9 Common Theoretical Models for Variable Structure State Estimation
506(1)
20.4.10 Automatic Tracking of Targets in Complex Environments
507(1)
20.4.11 Tracking and Invulnerability of Multi-radar Network Systems
507(1)
References 508(15)
Index 523
Dr You He, Professor and Chancellor of Naval Aeronautical and Astronautical University, China. Dr He received his Ph.D degree in electronic engineering from Tsinghua University, Beijing, P.R. China, in 1997. From Oct. 1991 to Nov. 1992, he was with the Institute of Communication at Technical University of Braunschweig, Germany. He is Fellow Member of the Chinese Institute of Electronic, Executive Director of China aviation society, and Director of the Information Fusion Branch of China Aviation Society. His research interests include detection and estimation theory, multiple target tracking and multisensor information fusion. He has been engaged in target tracking and information fusion research work for 30 years. He has published over two hundred journal papers and three books. In 2013, Dr. He was elected to be a member of Chinese Academy of Engineering. Dr. Jian-Juan Xiu received her Ph.D in Naval Aeronautical and Astronautical University, China, in 2004. Now she is an associate professor of the university. Her research interests include passive location, multiple target tracking and multi-sensor information fusion. Dr. Xin Guan received his Ph.D from Naval Aeronautical and Astronautical University in 2006. She is now a professor and master tutor in Department of Electronics and Communication of the same school. She is major in ECM, radar emitter identification and evidence theory. She has published over 70 papers and two academic monographs.
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