Radar Data Processing With Applications E-Book

He You

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 855

Veröffentlichungsjahr: 2016

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title Page

About the Authors

Preface

Acknowledgments

1 Introduction

1.1 Aim and Significance of Radar Data Processing

1.2 Basic Concepts in Radar Data Processing

1.3 Design Requirements and Main Technical Indexes of Radar Data Processors

1.4 History and Present Situation of Research in Radar Data Processing Technology

1.5 Scope and Outline of the Book

2 Parameter Estimation

2.1 Introduction

2.2 The Concept of Parameter Estimation

2.3 Four Basic Parameter Estimation Techniques

2.4 Properties of Estimators

2.5 Parameter Estimation of Static Vectors

2.6 Summary

3 Linear Filtering Approaches

3.1 Introduction

3.2 Kalman Filter

3.3 Steady‐State Kalman Filter

3.4 Summary

4 Nonlinear Filtering Approaches

4.1 Introduction

4.2 Extended Kalman Filter

4.3 Unscented Kalman Filter

4.4 Particle Filter

4.5 Summary

5 Measurement Preprocessing Techniques

5.1 Introduction

5.2 Time Registration

5.3 Space Registration

5.4 Radar Error Calibration Techniques

5.5 Data Compression Techniques

5.6 Summary

6 Track Initiation in Multi‐target Tracking

6.1 Introduction

6.2 The Shape and Size of Track Initiation Gates

6.3 Track Initiation Algorithms

6.4 Comparison and Analysis of Track Initiation Algorithms

6.5 Discussion of Some Issues in Track Initiation

6.6 Summary

7 Maximum Likelihood Class Multi‐target Data Association Methods

7.1 Introduction

7.2 Track‐Splitting Algorithm

7.3 Joint Maximum Likelihood Algorithm

7.4 0–1 Integer Programming Algorithm

7.5 Generalized Correlation Algorithm

7.6 Summary

8 Bayesian Multi‐target Data Association Approach

8.1 Introduction

8.2 Nearest‐Neighbor Algorithm

8.3 Probabilistic Data Association Algorithm

8.4 Integrated Probabilistic Data Association Algorithm

8.5 Joint Probabilistic Data Association Algorithm

8.6 Summary

9 Tracking Maneuvering Targets

9.1 Introduction

9.2 Tracking Algorithm with Maneuver Detection

9.3 Adaptive Tracking Algorithm

9.4 Performance Comparison of Maneuvering Target Tracking Algorithms

9.5 Summary

10 Group Target Tracking

10.1 Introduction

10.2 Basic Methods for Track Initiation of the Group Target

10.3 The Gray Fine Track Initiation Algorithm for Group Targets

10.4 Centroid Group Tracking

10.5 Formation Group Tracking

10.6 Performance Analysis of Tracking Algorithms for Group Targets

10.7 Summary

11 Multi‐target Track Termination Theory and Track Management

11.1 Introduction

11.2 Multi‐target Track Termination Theory

11.3 Track Management

11.4 Summary

12 Passive Radar Data Processing

12.1 Introduction

12.2 Advantages of Passive Radars

12.3 Passive Radar Spatial Data Association

12.4 Optimal Deployment of Direction‐Finding Location

12.5 Passive Location Based on TDOA Measurements

12.6 Summary

13 Pulse Doppler Radar Data Processing

13.1 Introduction

13.2 Overview of PD Radar Systems

13.3 Typical Algorithms of PD Radar Tracking

13.4 Performance Analysis on PD Radar Tracking Algorithms

13.5 Summary

14 Phased Array Radar Data Processing

14.1 Introduction

14.2 Characteristics and Major Indexes

14.3 Structure and Working Procedure

14.4 Data Processing

14.5 Performance Analysis of the Adaptive Sampling Period Algorithm

14.6 Summary

15 Radar Network Error Registration Algorithm

15.1 Introduction

15.2 The Composition and Influence of Systematic Errors

15.3 Fixed Radar Registration Algorithm

15.4 Mobile Radar Registration Algorithm

15.5 Summary

16 Radar Network Data Processing

16.1 Introduction

16.2 Performance Evaluation Indexes of Radar Networks

16.3 Data Processing of Monostatic Radar Networks

16.4 Data Processing of Bistatic Radar Networks

16.5 Data Processing of Multistatic Radar Networks

16.6 Track Association

16.7 Summary

17 Evaluation of Radar Data Processing Performance

17.1 Introduction

17.2 Basic Terms

17.3 Data Association Performance Evaluation

17.4 Performance Evaluation of Tracking

17.5 Evaluation of the Data Fusion Performance of Radar Networks

17.6 Methods of Evaluating Radar Data Processing Algorithms

17.7 Summary

18 Radar Data Processing Simulation Technology

18.1 Introduction

18.2 Basis of System Simulation Technology

18.3 Simulation of Radar Data Processing Algorithms

18.4 Simulation Examples of Algorithms

18.5 Summary

19 Practical Application of Radar Data Processing

19.1 Introduction

19.2 Application in ATC Systems

19.3 Application in Shipboard Navigation Radar

19.4 Application in Shipboard Radar Clutter Suppression

19.5 Application in Ground‐Based Radar

19.6 Applications in Shipboard Monitoring System

19.7 Application in the Fleet Air Defense System

19.8 Applications in AEW Radar

19.9 Application in Air Warning Radar Network

19.10 Application in Phased Array Radar

19.11 Summary

20 Review, Suggestions, and Outlook

20.1 Introduction

20.2 Review of Research Achievements

20.3 Issues and Suggestions

20.4 Outlook for Research Direction

References

Index

End User License Agreement

List of Tables

Chapter 04

Table 4.1 Comprehensive comparison of the three algorithms

Chapter 06

Table 6.1 The probability

P

G

that

n

z

‐dimensional measurements fall within the gate

Table 6.2 The ratio between the area/volume of the elliptic/ellipsoidal gate and that of the rectangular gate

Chapter 08

Table 8.1 Time consumed and false tracking rate

Chapter 09

Table 9.1 Target maneuvers in environment 1

Table 9.2 Target maneuvers in environment 2

Table 9.3 Target maneuvers in environment 2

Table 9.4 Comparison of the track lifetime and the average elapsed time of a cycle of the algorithms from environment 1 to environment 4

Chapter 10

Table 10.1 Value assignment for clutter and measurement error in environment 3

Table 10.2 Comparison of

P

Correct

and

P

Error

varying with the number of clutters between the algorithms

Table 10.3 Comparison of

P

Correct

and

P

Error

varying with measurement errors between the algorithms

Chapter 11

Table 11.1 Track termination time of each algorithm

Table 11.2 State difference equation for the

N

th initiation’s probability of success

Table 11.3 Criteria by which the initiation response time is smaller than the system index

Table 11.4 Probability of false track initiation (conditioned on

)

Table 11.5 False track life (

)

Table 11.6 Measurement missing probability and true track life

Table 11.7 Example of the correlation list of the fusion track

Chapter 13

Table 13.1 Simulation environment 1 parameter settings

Table 13.2 Simulation environment 2 parameter settings

Chapter 14

Table 14.1 Definitions of variables in flowchart

Table 14.2 Information on the target’s movement

Table 14.3 Comparison among position RMS, velocity RMS, and average period of constant gain filtering method

Table 14.4 Comparison among position RMS, velocity RMS, and average period of IMM algorithm

Table 14.5 Comparison among position RMS, velocity RMS, and average period of predicted covariance threshold algorithm

Chapter 15

Table 15.1 The systematic error estimation accuracy of the MLRM algorithm

Table 15.2 Collation map of MLRM and ASR systematic error estimation

Chapter 16

Table 16.1 Cartesian coordinates and observation error covariance corresponding to polar coordinates

Chapter 19

Table 19.1 Main parameters of the filtering algorithm

List of Illustrations

Chapter 01

Figure 1.1 Radar data processing relation diagram

Figure 1.2 Filtering diagram

Figure 1.3 Data processing flowchart

Chapter 02

Figure 2.1 Uniform cost function

Figure 2.2 Squared error cost function

Figure 2.3 Absolute value of error cost function

Figure 2.4 A posteriori probability density function

Chapter 03

Figure 3.1 Diagram of coordinate turn model

Figure 3.2 Discrete‐time linear system

Figure 3.3 Kalman filter algorithm

Figure 3.4 Single‐cycle flow of Kalman filter algorithm

Chapter 04

Figure 4.1 Principles of extended and unscented Kalman filters

Figure 4.2 Root mean square error of target position

Figure 4.3 Comparison of calculations

Figure 4.4 Simulation results in case 1

Figure 4.5 Simulation results in case 2

Chapter 05

Figure 5.1 Time registration

Figure 5.2 Right‐hand space rectangular coordinate system

Figure 5.3 Left‐hand space rectangular coordinate system

Figure 5.4 Space polar coordinate system

Figure 5.5 Earth coordinate system

Figure 5.6 NED coordinate system

Figure 5.7 Shipborne carrier coordinate system

Figure 5.8

ORED

and

OʹRʹEʹDʹ

Figure 5.9 Coordinate translation transformation

Figure 5.10 Rotation of single coordinate axes

Figure 5.11 Transformation of NED coordinate and shipborne coordinate system

Figure 5.12 Transformation of NED coordinate and earth rectangular coordinate system

Figure 5.13 Synthesis measurement of centralized radars

Chapter 06

Figure 6.1 The annular gate

Figure 6.2 Correlated wave gate in the rectangular coordinate system

Figure 6.3 Shape of the sector gate

Figure 6.4 The

m/n

logic of sliding window method

Figure 6.5 Straight line in the Cartesian coordinate system

Figure 6.6 Hough transform

Figure 6.7 Histogram in the parameter space

Figure 6.8 Angle restriction in track initiation

Figure 6.9 Situation map of clutter measurements and true measurements

Figure 6.10 Chart of the track initiated with direct‐vision method

Figure 6.11 Chart of the track initiated with 3/4 logic‐based method

Figure 6.12 Chart of the track initiated with modified logic‐based method

Figure 6.13 Chart of the track initiated with Hough transform‐based method

Figure 6.14 Chart of the track initiated with modified Hough transform method

Figure 6.15 Chart of the track initiated with Hough transform and logic‐based method

Figure 6.16 Situation map of clutter measurements and true measurements

Figure 6.17 Chart of the tracks initiated with direct‐vision method

Figure 6.18 Chart of the tracks initiated with 3/4 logic‐based method

Figure 6.19 Chart of the tracks initiated with modified 3/4 logic‐based method

Figure 6.20 Chart of the tracks initiated with Hough transform‐based method

Figure 6.21 Chart of the tracks initiated with modified Hough transform‐based method

Chapter 07

Figure 7.1 Single simulation cycle flowchart of the generalized correlation algorithm

Chapter 08

Figure 8.1 Real and filtering trajectory of the target

Figure 8.2 Enlarged version of Figure 8.1

Figure 8.3 RMS of the

x

axis (PDAF filtering)

Figure 8.4 RMS of the

y

axis (PDAF filtering)

Figure 8.5 Example of the validation matrix and the formation of association events

Figure 8.6 Association matrix block diagram

Figure 8.7 Real trajectories of the targets

Figure 8.8 RMS position errors of target 1 on axis

x

(top) and

y

(bottom)

Figure 8.9 RMS position errors of target 2 on axis

x

(top) and

y

(bottom)

Chapter 09

Figure 9.1 Schematic diagram of maneuvering target tracking

Figure 9.2 Structure chart of multiple model algorithm

Figure 9.3 Diagram of interacting multiple model algorithm

Figure 9.4 Target’s trajectory in environment 1

Figure 9.5 Comparison between Type 1 maneuvering target tracking algorithms

Figure 9.6 Comparison between Type 2 maneuvering target tracking algorithms

Figure 9.7 Comparison between maneuvering target tracking algorithms of Types 1 and 2

Figure 9.8 Target’s trajectory in environment 2

Figure 9.9 Comparison between Type 1 maneuvering target tracking algorithms

Figure 9.10 Comparison between Type 2 maneuvering target tracking algorithms

Figure 9.11 Comparison between maneuvering target tracking algorithms of Types 1 and 2

Figure 9.12 Target’s trajectory in environment 3

Figure 9.13 Comparison between Type 1 maneuvering target tracking algorithms

Figure 9.14 Comparison between Type 2 maneuvering target tracking algorithms

Figure 9.15 Comparison between maneuvering target tracking algorithms of Types 1 and 2

Figure 9.16 Target’s trajectory in environment 4

Figure 9.17 Comparison between Type 1 maneuvering target tracking algorithms

Figure 9.18 Comparison between Type 2 maneuvering target tracking algorithms

Figure 9.19 Comparison between maneuvering target tracking algorithms of Types 1 and 2

Figure 9.20 Target’s trajectory in environment 5

Figure 9.21 Target’s

x

‐axis RMS error

Figure 9.22 Target’s

y

‐axis RMS error

Chapter 10

Figure 10.1 Diagram for segmentation of the detection region

Figure 10.2 Statistical diagram of the number of measurements

Figure 10.3 Diagram for value assignment and calculation in the small region

Figure 10.4 Diagram for determination of the dense region of measurements

Figure 10.5 Diagram of association and distinction algorithm

Figure 10.6 Diagram of establishment of basic set and candidate set

Figure 10.7 Diagram of expansion of basic sets

Figure 10.8 Diagram of reduction of the number of candidate sets

Figure 10.9 Final basic set and candidate set

Figure 10.10 Framework for track initiation of group targets

Figure 10.11 Flowchart of the algorithm

Figure 10.12 Relative position of measurements in reference coordinate system

Figure 10.13 Measurement distribution diagram of pre‐association group

Figure 10.14 Targets’ overall situation (environment 1)

Figure 10.15 Measurements distribution at the first four moments (environment 1)

Figure 10.16 The real tracks of each target at the first four cycles (environment 1)

Figure 10.17 The real tracks of each target at the first four cycles (environment 2)

Figure 10.18 Comparison of track initiation of the three algorithms (environment 1)

Figure 10.19 Comparison of track initiation of the three algorithms (environment 2)

Figure 10.20 Comparison of overall initiation track qualities for the algorithms (environment 1)

Figure 10.21 Comparison of overall initiation track qualities for the algorithms (environment 2)

Figure 10.22 Comparison of overall initiation track accuracies for the algorithms (environment 1)

Figure 10.23 Comparison of overall initiation track accuracies for the algorithms (environment 2)

Figure 10.24 First four cycle measurements of group target (

,

)

Figure 10.25 First four cycle measurements distribution of group targets (

,

)

Figure 10.26 Tracks of the targets of 20 batches in environment 1

Figure 10.27 Comparison of filtering tracks of two group tracking algorithms

Figure 10.28 Comparison of RMS position errors in

x

axis for group 1

Figure 10.29 Comparison of RMS position errors in

x

axis for group 2

Figure 10.30 Comparison of RMS velocity errors in

x

axis for group 1

Figure 10.31 Comparison of RMS velocity errors in

x

axis for group 2

Figure 10.32 Comparison of algorithms’ single‐update durations varying with number of clutters

Figure 10.33 Comparison of algorithms’ correct association rates varying with number of clutters

Figure 10.34 Comparison of RMS errors in

x

axis in environment 2

Figure 10.35 Comparison of RMS velocity errors in

x

axis in environment 2

Chapter 11

Figure 11.1 Schematic diagram for radar observation region

Figure 11.2 Comparison of each algorithm’s false termination rate varying with the target batch number

Figure 11.3 Description of splitting tracks with the single‐track batch assignment method

Figure 11.4 The typical process of the double‐track batch descriptive method

Figure 11.5 Track batch assignment of the whole process including track initiation, maintenance, splitting, and mergence

Figure 11.6 The plane graph of the track batch

Figure 11.7 Description of typical track transformation process with track batch figure

Figure 11.8 Description of track splitting and mergence with the track batch figure

Figure 11.9 Solid figure

Figure 11.10 Significance of the track batch at the cancellation stage

Figure 11.11 Sketch map of unidirectional chained list storage of radar tracks

Figure 11.12 Sketch map of storage units in the sliding time window: (a)

; (b)

; (c)

Figure 11.13 Detection curve

Chapter 12

Figure 12.1 Difference of phase

Figure 12.2 Location principle diagram

Figure 12.3 Amplified diagram of location principle

Figure 12.4 Diagram of direction‐measuring cross locating under restricted conditions

Figure 12.5 Optimal cut angle

θ

CA

when

Figure 12.6 The target location distribution (on solid line and arc) when the area of the position concentration ellipse reaches the local minimum

Figure 12.7 Principle of location based on TDOA measurements in planes

Chapter 13

Figure 13.1 Frequency‐locked frequency tracking loop

Figure 13.2 Phase‐locked frequency tracker

Figure 13.3 Range tracking loop

Figure 13.4 (a) RMS position error and (b) RMS velocity error (environment 1, case 1)

Figure 13.5 (a) RMS position error and (b) RMS velocity error (environment 1, case 2)

Figure 13.6 (a) RMS position error and (b) RMS velocity error (environment 1, case 3)

Figure 13.7 (a) RMS position error and (b) RMS velocity error (environment 1, case 4)

Figure 13.8 (a) RMS position error and (b) RMS velocity error (environment 1, case 5)

Figure 13.9 (a) RMS position error, (b) RMS velocity error, and (c) average normalized estimation error squared (environment 2, case 1)

Figure 13.10 (a) RMS position error, (b) RMS velocity error, and (c) average normalized estimation error square (environment 2, case 2)

Figure 13.11 (a) RMS position error, (b) RMS velocity error, and (c) average normalized estimation error square (environment 2, case 3)

Figure 13.12 (a) RMS position error, (b) RMS velocity error, and (c) average normalized estimation error square (environment 2, case 4)

Figure 13.13 True movement track of target (environment 3)

Figure 13.14 (a) RMS position error and (b) RMS velocity error (environment 3)

Chapter 14

Figure 14.1 Structure of the phased array radar system

Figure 14.2 Working flowchart of phased array radar

Figure 14.3 Multi‐target tracking principle

Figure 14.4 IMM‐PDAF algorithm flowchart

Figure 14.5 Fixed template strategy

Figure 14.6 Multiple template strategy diagram

Figure 14.7 Partial template strategy diagram

Figure 14.8 Functions of the adaptive scheduling strategy

Figure 14.9 Target track

Figure 14.10 (a) Sampling period, (b) RMS position error, and (c) RMS velocity error of the constant gain filtering method

Figure 14.11 (a) Sampling period, (b) RMS position error, and (c) RMS velocity error of the IMM algorithm

Figure 14.12 (a) Sampling period, (b) RMS position error, and (c) RMS velocity error of the predicted covariance threshold algorithm

Chapter 15

Figure 15.1 Systematic errors and stochastic errors in radar measurement

Figure 15.2 Radar registration based on stereographic projection

Figure 15.3 Radar A’s systematic error estimation curve of ECEF‐LS algorithm

Figure 15.4 Radar B’s systematic error estimation curve of ECEF‐LS algorithm

Figure 15.5 Radar A’s systematic error estimation curve of ECEF‐GLS algorithm

Figure 15.6 Radar B’s systematic error estimation curve of ECEF‐GLS algorithm

Figure 15.7 The rotation relationship between the END and carrier coordinate systems

Figure 15.8 The latitude and longitude of the simulative environment

Figure 15.9 The measurements with system errors in mobile radars

Figure 15.10 Target state estimation effects of ASR algorithm on

x

axis

Figure 15.11 Target state estimation effects of ASR algorithm on

y

axis

Figure 15.12 Estimation effects of ASR algorithm on radar 1 range systematic error

Figure 15.13 Estimation effects of ASR algorithm on radar 1 azimuth systematic error

Figure 15.14 Estimation effects of ASR algorithm on radar 2 elevation systematic error

Figure 15.15 Estimation effects of ASR algorithm on radar 2 yaw angle systematic error

Figure 15.16 Estimation effects of ASR algorithm on radar 1 roll angle systematic error

Figure 15.17 Estimation effects of ASR algorithm on radar 2 pitch angle systematic error

Figure 15.18 Collation map of MLRM and ASR target state estimation

Chapter 16

Figure 16.1 The process of data processing of the monostatic radar network

Figure 16.2 Geometric relation of bistatic radar location

Figure 16.3 Schematic diagram of the MIMO radar

Figure 16.4 The multistatic radar observation under the main reference system

Chapter 17

Figure 17.1 Two cross‐moving targets

Figure 17.2 Two targets in “close and off” movement

Figure 17.3 Many targets in parallel motion

Chapter 18

Figure 18.1 S maneuver

Figure 18.2 Motorized dive

Figure 18.3 Pitch‐up maneuver

Figure 18.4 A comparison of the position error of target 1’s RMS on axis

x

Figure 18.5 A comparison of the position error of target 2’s RMS on axis

x

Figure 18.6 A comparison of the position error of target 1’s RMS on axis

x

Figure 18.7 A comparison of the position error of target 3’s RMS on axis

x

Figure 18.8 The true track of all the targets in environment 3

Figure 18.9 A change curve of the time consumed by the algorithm varying with average clutter number

Figure 18.10 A change curve of the correct association probability of the algorithm varying with average clutter number

Chapter 19

Figure 19.1 Relation between radar data processing and other systems

Figure 19.2 Centralized structure of ATC

Figure 19.3 Functional architecture of ATCCMS

Figure 19.4 Logic architecture of ATCCMS

Figure 19.5 Marine collision avoidance system

Figure 19.6 Tracking algorithm of Selenia collision avoidance system

Figure 19.7 Double parallel line patrol route

Figure 19.8 Data processing structure of the radar network

Figure 19.9 Screen of PPI display

Figure 19.10 Adaptive update rate

Figure 19.11 Split track tracking

Guide

Cover

Table of Contents

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RADAR DATA PROCESSING WITH APPLICATIONS

He You

Xiu Jianjuan

Guan Xin

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Library of Congress Cataloging‐in‐Publication Data

Names: You, He, 1956– author. | Jianjuan, Xiu, 1971– author. | Xin, Guan,1978– author.Title: Radar data processing with applications / He You, Xiu Jianjuan, Guan Xin.Description: Singapore : John Wiley & Sons, Inc., [2016] | Includes bibliographical references and index.Identifiers: LCCN 2016010486 | ISBN 9781118956861 (cloth) | ISBN 9781118956885 (epub) | ISBN 9781118956892 (Adobe PDF)Subjects: LCSH: Radar--Mathematics. | Radar–Data processing.Classification: LCC TK6578 .H425 2016 | DDC 621.38480285–dc23LC record available at https://lccn.loc.gov/2016010486

About the Authors

He You (Fellow of IET, Academician of Chinese Academy of Engineering) was born in Jilin Province, People’s Republic of China, in 1956. He received a Ph.D. from the Department of Electronic Engineering of Tsinghua University, Beijing, People’s Republic of China, in 1997. Then, he won a National Outstanding Doctoral Dissertation Award in 2000.

From October 1991 to November 1992, he was with the Institute of Communication at the Technical University of Braunschweig, Germany, as a senior visiting scholar researching automatic radar detection theory and constant false alarm rate processing. In December 1994, he joined the Naval Aeronautical and Astronautical University (NAAU) in Yantai, People’s Republic of China, as a Professor in the Department of Electronic Engineering, and engaged in research on signal processing and information fusion with applications. Now, he is Director of the Ministerial‐level Laboratory of Information Sensing and Fusion Technology, and Chief of the Information Fusion Research Institute, NAUU, as well. He has acquired over 20 authorized National Invention Patents, and is co‐author of more than 200 peer‐reviewed technical articles. Moreover, he is first author of the books Radar Target Detection and CFAR Processing (Tsinghua University Press, 1st edition 1999 and 2nd edition 2011), Multi‐sensor Information Fusion with Applications (Publishing House of Electronics Industry, 1st edition 2000 and 2nd edition 2007), Radar Data Processing with Application (Publishing House of Electronics Industry, 1st edition 2006, 2nd edition 2009, 3rd edition 2013, and translated into English), Information Fusion Theory with Application (Publishing House of Electronics Industry, 2010). These published books and papers have been cited more than 7000 times by other scholars. He has provided leadership in many research projects and gained significant scientific research achievements including three 2nd Awards of National Science and Technology Progress, one 1st Award and one 2nd Award of National Teaching Achievements. He is leader of the Information Fusion Team, which has been ranked as Ministerial‐level Innovation Team of Science and Technology, as well as Excellence Innovation Team of Shandong Province.

Dr. He has served as a Fellow of IET, Committee Member of National “863” Experts, Member of National Radar Detection Technology Group, Standing Director of Chinese Society of Aeronautics and Astronautics (CSAA), Founder and Chairman of Information Fusion Branch in CSAA, Standing Director of Chinese Society of Command and Control, Fellow of Chinese Institute of Electronics (CIE), Vice Chairman of Radio Positioning Technology Branch in CIE, and so on. He is a Vice Chairman on the Editorial Boards of Ship Electronic Engineering, Radar Science and Technology, and Fire Control & Command Control. He has also been appointed a Member on the Editorial Boards of Chinese Journal of Aeronautics (in English), Acta Aeronautica et Astronautica Sinica, Signal Processing (China), Journal of Radars, Journal of Data Acquisition & Processing, and so on.

Xiu Jianjuan was born in Shandong Province, People's Republic of China, in April 1971. She received her master and Ph.D. degree from Naval Aeronautical and Astronautical University, Yantai, People's Republic of China, in 2000 and 2004. She is now a professor in Research Institute of Information Fusion of Naval Aeronautical and Astronautical University. His research interests include radar data processing and passive location.

Guan Xin was born in Jinzhou, Liaoning province, People's Republic of China, in 1978. She received her bachelor degree in communication engineering from Liaoning University, Liaoning, People's Republic of China, in 1999 and received master and PhD degree from Naval Aeronautical and Astronautical University in 2002 and 2006, respectively. She is now a professor and doctor tutor in Department of Electronics and Communication of Naval Aeronautical and Astronautical University. She also serves as a director of Chinese institute of command and control and a senior member of Chinese Aviation Society. She is major in target identification and evidence reasoning, and has published over 80 papers and 3 academic monographs.

Preface

Advances in radar technology and application demands have promoted the fast development of radar signal processing and data processing technology. In recent years, with the continual emergence of new types of radar, significant progress has been made in related hardware, algorithms, and computer performance, and the signal processing capacity has been constantly improved, which demands the application of new algorithms in related radar data processing equipment to implement the simultaneous processing of multiple targets in the cluttered environments and allow the data association and tracking of multiple targets and information fusion of multiple radars in complex environments. That is why we decided to publish Radar Data Processing with Applications.

This book begins with the basic linear and nonlinear filtering approaches, and introduces the development and latest research findings on radar data processing technology thoroughly and systematically. Its main contents are as follows.

The initial discussion deals with the static and dynamic parameter estimation for linear and nonlinear discrete‐time systems, providing such classical filtering algorithms as the Kalman filter, the extended Kalman filter, the unscented Kalman filter, and the particle filter.

Measurement preprocessing techniques are discussed, including time and space registration, radar error correction, and data compression.

Such practical issues as multi‐target track initiation, data association, and tracking are introduced, of which multi‐target data association is divided into the maximum likelihood and Bayesian approach. Maneuvering target tracking, group target tracking, and track termination are also discussed.

The final analysis is the practical application of radar data processing, including passive radar data processing, pulse Doppler radar data processing, phased array radar data processing, radar network error registration, radar network data processing, radar data processing performance evaluation, and simulation techniques.

Acknowledgments

The authors gratefully acknowledge the contributions of those colleagues from the English Department who have been involved in the translation work: Associate Prof. Chen Li, Associate Prof. Yang An‐liang, Associate Prof. Liu Hong‐ying, Lecturer Liu Hui, Lecturer Qu Lei, Lecturer Wang Xue‐sheng, Lecturer Xu Xiao‐juan, Lecturer Zhang Dong‐li, Lecturer Zhu Zi‐jian, and Lecturer Guan Hui‐jie. The authors would like to express their appreciation to Dr. Dong Kai, Dr. Wang Hai‐peng, Dr. Cui Ya‐qi, and postgraduates Miao Xu‐bin, Wang Wang‐song, and Sun Shun for their participation in proofreading and revision. Special thanks go to the Electronic Industry Publishing House, especially to Editor Qu Xin, for support in the publication of this book.

It is expected that the publication of this book will not only provide a very readable reference for those engaged in information engineering, pattern recognition, military command, etc., but also lay a theoretical foundation for their work and further study.

Any advice and suggestions from readers of this book are most welcome.

1Introduction

1.1 Aim and Significance of Radar Data Processing

Generally, a modern radar system consists of two important components: a signal processor and a data processor. The signal processor is used for target detection (i.e., the suppression of undesirable signals produced by ground or sea surface clutter, meteorological factors, radio frequency interference, noise sources, and man‐made interference) [1–3]. When the video output signal, after signal processing and constant false alarm rate (CFAR) detection fusion, exceeds a certain detection threshold, it can be determined that a target has been discovered. Then, the discovered target signal will be transmitted to the data recording device, where the space position, amplitude value, radial velocity, and other characteristic parameters of the target are recorded, usually by computers. The measurement output from the data recording device needs to be processed in the data processor, which associates, tracks, filters, smooths, and predicts the obtained measurement data – such as the target position (radial distance, azimuth, and pitch angle) and the motion parameters [4–6] – for the effective suppression of random errors occurring during the measurement, estimation of the trajectory and related motion parameters (velocity and acceleration, etc.) of the target in the control area, prediction of the target’s position at the next moment, and formation of a steady target track, so that highly accurate real‐time tracking is realized [7–9].

In terms of the level at which radar echo signals are processed, radar signal processing is usually viewed as the primary processing of the information detected by the radar unit. It is done at each radar station, with information obtained from the same radar and the same scanning period and distance unit, with the aim of extracting useful target information from clutter, noise, and various active and passive jamming backgrounds. Radar data processing is usually viewed as secondary processing of the radar information [10–13]. Making use of information from the same radar, but with different scanning periods and distance units, it can be done both at each independent radar station and at the information processing center or system command center of the radar network. Data fusion of multiple radars can be viewed as a third or tertiary processing of the radar information, which is usually done at the information processing center. Specifically, the information the processing center receives is the measurement from the primary processing or the track from the secondary processing (usually called the local track) by multiple radars, and the track after fusion (called the global track or system track). The function of the secondary processing of radar information, based on the primary processing, is to filter and track several targets, and estimate the targets’ motion parameters and characteristic parameters. Secondary processing is done strictly after primary processing, while there is no strict time limit between secondary and tertiary processing. The third level of processing is the expansion and extension of secondary processing, which is mainly reflected in space and dimension.

1.2 Basic Concepts in Radar Data Processing

The input to the radar data processing unit is the measurement from the front, which is the object of data processing, while the output is the track formed after data processing is conducted. Generally, functional modules of radar data processing include measurement pretreatment, track initiation and termination, and data association and tracking. A wave gate must be set up between the association and the tracking process, and their relationship is shown in the block diagram in Figure 1.1. The content and related concepts of the functional modules of radar data processing are briefly discussed as follows.

Figure 1.1 Radar data processing relation diagram

1.2.1 Measurements

Measurements, also called observations, refer to noise‐corrupted observations related to the state of a target [14]. The measurements are not usually raw data points, but the output from the data recording device after signal processing. Measurements can be divided, according to whether they are associated with the known target track, into free measurements and correlated measurements. Free measurements are spots that are not correlated with the known target track, while correlated measurements are spots that are correlated with the known target track.

1.2.2 Measurement Preprocessing

Although modern radar adopts many signal processing technologies, there will always be a small proportion of clutter/interference signals left out. To relieve the computers doing the follow‐up processing job from a heavy burden, prevent computers from saturation, and improve system performance, the measurement given by the primary processing needs to be preprocessed, which is called “measurement preprocessing”: the preprocessing of secondary processing of radar information. The preprocessing is a precondition of correct processing of radar data, since an effective measurement data processing method can actually help yield twice the result with half the effort, with the target tracking accuracy improved while the computational complexity of the target tracking is reduced. The measurement preprocessing technology mainly involves system error registration, time synchronization, space alignment, outlier rejection, and saturation prevention.

1.2.2.1 System Error Registration

The measurement data from radars contains two types of error. One is random error, resulting from the interior noise of the measurement system. Random error may vary with each measurement, and may be eliminated to some extent by increasing the frequency of measurement and minimizing its variance in the statistical sense by means of methods like filtering. The other is system error, resulting from measurement environments, antennas, servo systems, and such non‐calibration factors in the data correction process as the position error of radar stations and the zero deviation of altimeters. System error is complex, slowly varying, and non‐random, and can be viewed as an unknown variable in a relatively long period of time. As indicated by the findings in Ref. [15], when the ratio of system errors to random errors is greater than or equal to 1, the effect of distributed track fusion and centralized measurement fusion deteriorates markedly, and at this point system errors must be corrected.

1.2.2.2 Time Synchronization

Owing to the possible difference in each radar’s power‐on time and sampling rate, the target measurement data recorded by data recording devices may be asynchronous. Therefore, these observation data must be synchronized in multiple‐radar data processing. Usually, the sampling moment of a radar is set as the benchmark for the time of other radars.

1.2.2.3 Space Alignment

Space alignment is the process of unifying the coordinate origin, coordinate axis direction, etc. of the data from the radar stations in different places, so as to bring the measurement data from several radars into a unified reference framework, paving the way for the follow‐up radar data processing.

1.2.2.4 Outlier Rejection

Outlier rejection is the process of removing the obviously abnormal values from radar measurement data.

1.2.2.5 Saturation Prevention

Saturation prevention mainly deals with saturation in the following two cases.

In the design of a data processing system, there is a limit to the number of target data. However, in a real system, saturation occurs when the data to be processed exceed the processing capacity.

The time used to process data is limited. Saturation occurs when the number of measurements, or batches of targets, reaches a certain extent. In this case, the processing of the data from one observation has to be interrupted before the processor starts to deal with the next batch of data.

1.2.3 Data Association

In the single‐target, clutter‐free environment, where there is only one measurement in the target‐related wave gate, only tracking is involved. Under multi‐target circumstances, where a single measurement falls in the intersection area of several wave gates or several measurements fall in the related wave gate of a single target, data association is involved. For instance, suppose two target tracks have been established before the radar’s nth scanning, and two echoes are detected in the nth scanning, are the echoes from two new targets or from the two established tracks at that time? If they are from the two established tracks at that time, then in what way can the echoes resulting from the two scans and the two tracks be correctly paired? The answer involves data association, the establishment of the relationship between the radar measurements at a given moment and the measurements (or tracks) at other moments, to check whether these measurements originate from the processing of the same target (or to ensure a correct process of measurement‐and‐track pairing).

Data association, also called “data correlation” or “measurement correlation,” is a crucial issue in radar data processing. False data association could pair the target with a false velocity, which could result in the collision of aircraft with air traffic control radars, or the loss of target interception with military radars. Data association is realized through related wave gates, which exclude the true measurements of other targets and the false measurements of noise and interference.

Generally, data association can be categorized, according to what is being associated with what, into the following classes [16]:

measurement‐to‐measurement (track initiation);

measurement‐to‐track (track maintenance or track updating);

track‐to‐track, also called track correlation (track fusion).

1.2.4 Wave Gate

In the process of target track initiation and tracking, a wave gate is often used to solve data association problems. What then is a wave gate? How many categories is it divided into? A brief discussion of these questions follows.

An initial wave gate is a domain centering on free measurements, used to determine the region where the target’s observations may occur. At the track initiation stage, the initial wave gate is normally bigger for better target acquisition.

A correlation wave gate (or tracking wave gate, validation gate) is a domain centering on the predicted position of the tracked target, used to determine the region where the target’s observations may occur [17].

The size of the wave gate is related to the magnitude of radar measurement error, the probability of correct echo reception, etc. That is to say, when deciding the wave gate’s shape and size, one should make it highly probable that the true measurement falls in the wave gate, while making sure that there are not many unrelated measurements in the correlation wave gate. The echo falling in the correlation wave gate is called a candidate echo. The size of the tracking gate reflects the error in the predicted target position and velocity, which is related to the tracking method, radar measurement error, and required correct correlation rate. The size of the correlation wave gate is not fixed in the tracking process, but adaptive adjustment should be made among small, medium, and large wave gates in accordance with the tracking conditions.

For a target in uniform rectilinear motion (e.g., a civil airliner flying smoothly at high altitude), a small wave gate should be set up, with its minimum size no less than three times the mean square root value of the measurement error.

When the target maneuver is relatively small (e.g., when the aircraft is taking off, landing, or making a slow turn), a medium wave gate should be set up, by adding one or two times the mean square root value of the measurement error to the small wave gate.

When the target maneuver is relatively big (e.g., when the aircraft is making a fast turn, or when the target is lost and recaptured), a large wave gate should be set up. Besides, at the track initiation stage, a large wave gate should be adopted to effectively capture the target’s initial wave gate.

1.2.5 Track Initiation and Termination

Track initiation refers to the process from the entrance (and detection) of a target into the radar coverage area to the establishment of the target track. Target initiation is important in radar data processing. If the track initiation is incorrect, target tracking is impossible.

Since the target being tracked may escape the surveillance zone at any time, once it goes beyond the radar detection range, the tracker must make relevant decisions to eliminate the unwanted track files for track termination.

1.2.6 Tracking

Tracking is one of the two primary issues in radar data processing. It refers to the processing of the target’s measurements for the constant estimation of the target’s current state [16]. The multiple‐radar and multi‐target tracking system is a highly complex large‐scale system, whose complexity is mainly due to the uncertainty in radar data processing.

From the perspective of measurement data, the received radar measurements form a random sequence, which may be obtained by non‐equal interval sampling, and the observation noises are non‐Gaussian. This should be considered in real measurement data processing.

From the perspective of multi‐target tracking, the complexity of the tracking problem lies mainly in:

the uncertainty of measurement origin – since there are multiple targets and false alarms, many measurements may be produced in radar environments, which will lead to the uncertainty of the measurements used for filtering;

the uncertainty of the target model parameter – since targets could be on maneuvers at any time, the model parameter initially set could be incorrect. Therefore, adjustments must be made to the model parameter in accordance with the tracking conditions; hence maneuvering target tracking.

From the perspective of the system, the tracking system could be nonlinear, with a complex construction. On the one hand, the system tracking performance under complex circumstances depends chiefly on the filtering algorithm’s capability to deal with the uncertainty of measurement origins and target model parameters, or its capability to effectively solve the problem of measurement correlation and adaptive target tracking. On the other hand, the nonlinear characteristics of the system itself should also be taken into consideration.

For the effective tracking of the target under these complex circumstances, the following two problems need to be solved.

First, the establishment of the target motion model and the observation model. Estimation theory, which provides a foundation for radar data processing, requires the establishment of a system model describing the dynamic characteristics of target and radar measurement processes. A valuable method of describing the system model, the state variable method, is based on the system state equation and the observation equation. According to this method, the state variable, system state equation, system observation equation, system noise and observation noise, system input and output (i.e., the estimated value of the state variable) are the five essential elements of the target tracking system modeling. The five elements above reflect the basic characteristics of a system, and can be viewed as a complete expression of a dynamic system. The introduction of the state variable is the core of creating an optimum control and estimation theory, because in the state space, the state variable defined should be a batch of variables with minimum dimensions that can fully reflect the system dynamic characteristics. The state variable at any given time is expressed as a function of the state variable prior to that time, and the input/output relationship of the system is described by the state transition model and the output observation model in the time domain. The state reflects the system’s “interior condition.” The input can be described by the state equation, which is composed of the decided time function and the random process representing the unpredictable variable or noise. The output is a function of the state vector, usually disturbed by the random observation error, and can be described by measurement equations. In the system modeling process, the use of the system state equation and the observation equation in the description of the dynamic characteristics of the target is therefore the most successful method in common use. The relation between the state equation and the measurement equation is shown in Figure 1.2.

Figure 1.2 Filtering diagram

Second, the tracking algorithm. The tracking filtering algorithm in the state space is actually a matter of optimum estimation based on state space. The following two points are of major concern.

Multiple maneuvering target tracking. Maneuvers are both the basic attribute of the target and the forms of motion commonly used in attacks or escapes. Therefore, maneuvering multi‐target tracking is the focus of target tracking, dealing with the problem of a maneuvering target model, testing and tracking algorithm.

The optimality, robustness, and rapidity of tracking algorithms. That is to say, an overall consideration is needed of the tracking timeliness, tracking accuracy, and robustness of the algorithm.

1.2.7 Track

A track is a trajectory which is formed with the states of a target estimated from a set of measurements of the same target (i.e., tracking trajectory). The radar, when conducting multi‐target data processing, designates an identity (ID) for each tracking trajectory, namely the track ID, which serves as a point of reference for all the parameters related to a given track. The measurement of the track’s reliability can be described by the track quality which, if properly controlled, can help both promptly and accurately initiate a track so that a new target file is set up, and cancel a track so that the redundant target files are cleared up. Tracks are the ultimate result of data processing, as shown in Figure 1.3.

Figure 1.3 Data processing flowchart

The concepts related to tracks also include the following.

Possible track.

The possible track is a track composed of a single measurement point.

Tentative track.

Tentative tracks are tracks composed of two or more measurement points with low track quality. They could be target tracks, or random interference, namely false tracks. After initial correlation is complete, a possible track is turned into a tentative track or a canceled track. The tentative track is also called a temporary track.

Confirmed track.

A confirmed track, also called a reliable track or a stable track, is a track with stable output or a track whose track quality exceeds a given value. It is the formal track set up by the data processor, and is generally considered as a true target track.

Fixed track.

A fixed track is a track composed of clutter measurements, whose position does not change much with the scans of a radar set.

The following sequence can be determined in the correlation process of measurements and tracks: fixed tracks first, then reliable tracks, and finally tentative tracks. That is to say, after a batch of observation measurements is obtained, the correlation of these measurements and the fixed track is done first. The measurements that can be correlated with the fixed track are deleted from the measurement file and are used to update the fixed track (i.e., to replace the old clutter points with the measurements that are correlated). If these measurements cannot be correlated with the fixed track, they should be correlated with the existing confirmed track. The successfully correlated measurements are used to update the confirmed track. The measurements that cannot be correlated with the confirmed track should be correlated with the tentative track, which finally either disappears or is turned into a confirmed track or a fixed track. The confirmed track has priority over the tentative track, which excludes the possibility that the tentative track obtains measurements from the reliable track.

Canceled track.

When its quality is lower than a given value or is composed of isolated random interference points, the track is called a canceled track, and the process is called track cancellation or track termination. Track cancellation is the process of erasing the track when it does not conform to a certain rule, which means the track is not a track of a true target, or that the corresponding target has moved out of the radar coverage range. Specifically, when a certain track cannot be correlated with any measurement in a certain scan, an extrapolation should be done according to the latest velocity. Any track that does not receive a measurement in a certain number of successive scans should be canceled. The primary task of track cancellation is to promptly cancel a false track with the true one being retained.

There are three possible instances of track cancellation.

Possible tracks (with only track heads) to be canceled as long as there is no measurement in the first scanning period that follows them.

Tentative tracks (such as a newly initiated track) to be erased from the database as long as there is no measurement in the three successive scanning periods that follow them.

Confirmed tracks, whose cancellation should be done with caution. If no measurement falls in the relevant wave gates in four to six successive scanning periods, cancellation of the track can be considered. It is worth noting that extrapolation must be used several times to expand the wave gates to recapture the lost target. Of course, track quality management can also be used to cancel a track.

Redundant tracks.

Two or more tracks being allocated to the same true target is called track redundancy. The unnecessary track is called a redundant track.

Track interruption.

If a certain track is allocated to a true target at time

t

, but no track is allocated to the target at time

, then track interruption happens at time

t

, where

m

is a parameter set by the tester, usually

.

Track switch.

If a certain track is allocated to a true target at time

t

, while another track is allocated to the target at time

, then track switch happens at time

t

, where

m

is a parameter set by the tester, usually

.

Track life

(the length of a track; the times the track is successively correlated). Based on whether the terminated track is false or true, it can be divided into [18, 19]:

False track life.

The average times of radar scanning from the initiation of a false track to its deletion is called false track life. False track can sometimes last for a long time when false measurements are highly dense.

True track life.

The average times of radar scanning of a true track mistaken for a false one and deleted after it is initiated.

True track maintenance time is restricted by two factors: