Preface ........................................................ xv
Author ........................................................ xix
Introduction .................................................. xxi
PART I Design of Radar Digital Signal Processing and Control
Algorithms
Chapter 1 Principles of Systems Approach to Design Complex
Radar Systems ................................................... 3
1.1 Methodology of Systems Approach ............................ 3
1.2 Main Requirements of Complex Radar Systems ................. 6
1.3 Problems of System Design for Automated Complex Radar
Systems ................................................... 13
1.4 Radar Signal Processing System as an Object of Design ..... 15
1.5 Summary and Discussion .................................... 21
References ..................................................... 23
Chapter 2 Signal Processing by Digital Generalized Detector
in Complex Radar Systems ....................................... 25
2.1 Analog-to-Digital Signal Conversion: Main Principles ...... 25
2.1.1 Sampling Process ................................... 25
2.1.2 Quantization and Signal Sampling Conversion ........ 29
2.1.3 Analog-to-Digital Conversion: Design Principles
and Main Parameters ................................ 30
2.1.3.1 Sampling and Quantization Errors .......... 30
2.1.3.2 Reliability ............................... 32
2.2 Digital Generalized Detector for Coherent Impulse
Signals ................................................... 32
2.2.1 Matched Filter ..................................... 32
2.2.2 Generalized Detector ............................... 34
2.2.3 Digital Generalized Detector ....................... 36
2.3 Convolution in Time Domain ................................ 39
2.4 Convolution in Frequency Domain ........................... 47
2.5 Examples of Some DGD Types ................................ 52
2.6 Summary and Discussion .................................... 53
References ..................................................... 55
Chapter 3 Digital Interperiod Signal Processing Algorithms .... 57
3.1 Digital Moving-Target Indication Algorithms ............... 57
3.1.1 Principles of Construction and Efficiency Indices .. 57
3.1.2 Digital Rejector Filters ........................... 60
3.1.3 Digital Moving-Target Indicator in Radar System
with Variable Pulse Repetition Frequency ........... 66
3.1.4 Adaptation in Digital Moving-Target Indicators ..... 67
3.2 DGD for Coherent Impulse Signals with Known Parameters .... 69
3.2.1 Initial Conditions ................................. 69
3.2.2 DGD for Target Return Pulse Train .................. 72
3.2.3 DGD for Binary Quantized Target Return Pulse
Train .............................................. 74
3.2.4 DGD Based on Methods of Sequential Analysis ........ 75
3.2.5 Software DGD for Binary Quantized Target Return
Pulse Train ........................................ 81
3.3 DGD for Coherent Impulse Signals with Unknown Parameters .. 82
3.3.1 Problem Statements of Digital Detector Synthesis ... 82
3.3.2 Adaptive DGD ....................................... 84
3.3.3 Nonparametric DGD .................................. 87
3.3.3.1 Sign-Nonparametric DGD .................... 88
3.3.3.2 Rank-Nonparametric DGD .................... 89
3.3.4 Adaptive-Nonparametric DGD ......................... 91
3.4 Digital Measurers of Target Return Signal Parameters ...... 93
3.4.1 Digital Measurer of Target Range ................... 94
3.4.2 Algorithms of Angular Coordinate Estimation under
Uniform Radar Antenna Scanning ..................... 95
3.4.3 Algorithms of Angular Coordinate Estimation under
Discrete Radar Antenna Scanning ................... 100
3.4.4 Doppler Frequency Measurer ........................ 103
3.5 Complex Generalized Algorithms of Digital Interperiod
Signal Processing ........................................ 105
3.6 Summary and Discussion ................................... 108
References .................................................... 111
Chapter 4 Algorithms of Target Range Track Detection and
Tracking ...................................................... 115
4.1 Main Stages and Signal Reprocessing Operations ........... 117
4.1.1 Target Pip Gating: Shape Selection and
Dimensions of Gates ............................... 119
4.1.2 Algorithm of Target Pip Indication by Minimal
Deviation from Gate Center ........................ 122
4.1.3 Target Pip Distribution and Binding within
Overlapping Gates ................................. 125
4.2 Target Range Track Detection Using Surveillance Radar
Data ..................................................... 128
4.2.1 Main Operations under Target Range Track
Detection ......................................... 128
4.2.2 Statistical Analysis of "2m + 1/n" Algorithms
under False Target Range Track Detection .......... 129
4.2.3 Statistical Analysis of "2m + 1/n" Algorithms
under True Target Range Track Detection ........... 135
4.3 Target Range Tracking Using Surveillance Radar Data ...... 138
4.3.1 Target Range Autotracking Algorithm ............... 138
4.3.2 United Algorithm of Detection and Target Range
Tracking .......................................... 142
4.4 Summary and Discussion ................................... 143
References .................................................... 146
Chapter 5 Filtering and Extrapolation of Target Track
Parameters Based on Radar Measure ............................. 149
5.1 Initial Conditions ....................................... 150
5.2 Process Representation in Filtering Subsystems ........... 150
5.2.1 Target Track Model ................................ 150
5.2.2 Measuring Process Model ........................... 153
5.3 Statistical Approach to Solution of Filtering Problems
of Stochastic (Unknown) Parameters ....................... 155
5.4 Algorithms of Linear Filtering and Extrapolation under
Fixed Sample Size of Measurements ........................ 156
5.4.1 Optimal Parameter Estimation Algorithm by
Maximal Likelihood Criterion for Polynomial
Target Track: A General Case ...................... 157
5.4.2 Algorithms of Optimal Estimation of Linear
Target Track Parameters ........................... 159
5.4.3 Algorithm of Optimal Estimation of Second-Order
Polynomial Target Track Parameters ................ 162
5.4.4 Algorithm of Extrapolation of Target Track
Parameters ........................................ 166
5.4.5 Dynamic Errors of Target Track Parameter
Estimation Using Polar Coordinate System .......... 168
5.5 Recurrent Filtering Algorithms of Undistorted
Polynomial Target Track Parameters ....................... 170
5.5.1 Optimal Filtering Algorithm Formula Flowchart ..... 170
5.5.2 Filtering of Linear Target Track Parameters ....... 174
5.5.3 Stabilization Methods for Linear Recurrent
Filters ........................................... 177
5.5.3.1 Introduction of Additional Term into
Correlation Matrix of Extrapolation
Errors ................................... 178
5.5.3.2 Introduction of Artificial Aging of
Measuring Errors ......................... 179
5.5.3.3 Gain Lower Bound ......................... 179
5.6 Adaptive Filtering Algorithms of Maneuvering Target
Track Parameters ......................................... 179
5.6.1 Principles of Designing the Filtering
Algorithms of Maneuvering Target Track
Parameters ........................................ 179
5.6.1.1 First Approach ........................... 180
5.6.1.2 Second Approach .......................... 181
5.6.1.3 Third Approach ........................... 181
5.6.2 Implementation of Mixed Coordinate Systems under
Adaptive Filtering ................................ 181
5.6.3 Adaptive Filtering Algorithm Version Based on
Bayesian Approach in Maneuvering Target ........... 186
5.7 Logical Flowchart of Complex Radar Signal Reprocessing
Algorithm ................................................ 192
5.8 Summary and Discussion ................................... 193
References .................................................... 199
Chapter 6 Principles of Control Algorithm Design for
Complex Radar System Functioning at Dynamical Mode ............ 201
6.1 Configuration and Flowchart of Radar Control Subsystem ... 202
6.2 Direct Control of Complex Radar Subsystem Parameters ..... 207
6.2.1 Initial Conditions ................................ 207
6.2.2 Control under Directional Scan in Mode of
Searched New Targets .............................. 207
6.2.3 Control Process under Refreshment of Target in
Target Tracing Mode ............................... 211
6.3 Scan Control in New Target Searching Mode ................ 213
6.3.1 Problem Statement and Criteria of Searching
Control Optimality ................................ 213
6.3.2 Optimal Scanning Control under Detection of
Single Target ..................................... 214
6.3.3 Optimal Scanning Control under Detection of
Unknown Number of Targets ......................... 215
6.3.4 Example of Scanning Control Algorithm in Complex
Radar Systems under Aerial Target Detection and
Tracking .......................................... 219
6.4 Power Resource Control under Target Tracking ............. 222
6.4.1 Control Problem Statement ......................... 222
6.4.2 Example of Control Algorithm under Target
Tracking Mode ..................................... 223
6.4.3 Control of Energy Expenditure under Accuracy
Aligning .......................................... 226
6.5 Distribution of Power Resources of Complex Radar System
under Combination of Target Searching and Target
Tracking Modes ........................................... 228
6.6 Summary and Discussion ................................... 231
References .................................................... 233
PART II Design Principles of Computer System for Radar
Digital Signal Processing and Control Algorithms
Chapter 7 Design Principles of Complex Algorithm
Computational Process in Radar Systems ........................ 237
7.1 Design Considerations .................................... 237
7.1.1 Parallel General-Purpose Computers ................ 238
7.1.2 Custom-Designed Hardware .......................... 239
7.2 Complex Algorithm Assignment ............................. 241
7.2.1 Logical and Matrix Algorithm Flowcharts ........... 241
7.2.2 Algorithm Graph Flowcharts ........................ 243
7.2.3 Use of Network Model for Complex Algorithm
Analysis .......................................... 246
7.3 Evaluation of Work Content of Complex Digital Signal
Processing Algorithm Realization by Microprocessor
Subsystems ............................................... 249
7.3.1 Evaluation of Elementary Digital Signal
Processing Algorithm Work Content ................. 249
7.3.2 Definition of Complex Algorithm Work Content
Using Network Model ............................... 250
7.3.3 Evaluation of Complex Digital Signal
Reprocessing Algorithm Work Content in Radar
System ............................................ 252
7.4 Paralleling of Computational Process ..................... 257
7.4.1 Multilevel Graph of Complex Digital Signal
Processing Algorithm .............................. 257
7.4.2 Paralleling of Linear Recurrent Filtering
Algorithm Macro-Operations ........................ 263
7.4.3 Paralleling Principles of Complex Digital Signal
Processing Algorithm by Object Set ................ 265
7.5 Summary and Discussion ................................... 267
References .................................................... 271
Chapter 8 Design Principles of Digital Signal Processing
Subsystems Employed by a Complex Radar System ................. 273
8.1 Structure and Main Engineering Data of Digital Signal
Processing Subsystems .................................... 273
8.1.1 Single-Computer Subsystem ......................... 273
8.1.2 Multicomputer Subsystem ........................... 276
8.1.3 Multimicroprocessor Subsystems for Digital
Signal Processing ................................. 278
8.1.4 Microprocessor Subsystems for Digital Signal
Processing in Radar ............................... 280
8.2 Requirements for Effective Speed of Operation ............ 282
8.2.1 Microprocessor Subsystem as a Queuing System ...... 282
8.2.2 Functioning Analysis of Single-Microprocessor
Control Subsystem as Queuing System ............... 285
8.2.3 Specifications for Effective Speed of
Microprocessor Subsystem Operation ................ 289
8.3 Requirements for RAM Size and Structure .................. 293
8.4 Selection of Microprocessor for Designing the
Microprocessor Subsystems ................................ 295
8.5 Structure and Elements of Digital Signal Processing and
Complex Radar System Control Microprocessor Subsystems ... 296
8.6 High-Performance Centralized Microprocessor Subsystem
for Digital Signal Processing of Target Return Signals
in Complex Radar Systems ................................. 299
8.7 Programmable Microprocessor for Digital Signal
Preprocessing of Target Return Signals in Complex Radar
Systems .................................................. 301
8.8 Summary and Discussion ................................... 302
References .................................................... 306
Chapter 9 Digital Signal Processing Subsystem Design
(Example) ..................................................... 309
9.1 General Statements ....................................... 309
9.2 Design of Digital Signal Processing and Control
Subsystem Structure ...................................... 310
9.2.1 Initial Statements ................................ 310
9.2.2 Main Problems of Digital Signal Processing
and Control Subsystem ............................. 311
9.2.3 Central Computer System Structure for Signal
Processing and Control ............................ 314
9.3 Structure of Coherent Signal Preprocessing
Microprocessor Subsystem ................................. 315
9.4 Structure of Noncoherent Signal Preprocessing
Microprocessor Subsystem ................................. 318
9.4.1 Noncoherent Signal Preprocessing Problems ......... 318
9.4.2 Noncoherent Signal Preprocessing Microprocessor
Subsystem Requirements ............................ 321
9.5 Signal Reprocessing Microprocessor Subsystem
Specifications ........................................... 322
9.6 Structure of Digital Signal Processing Subsystem ......... 325
9.7 Summary and Discussion ................................... 327
References .................................................... 329
Chapter 10 Global Digital Signal Processing System Analysis ... 331
10.1 Digital Signal Processing System Design .................. 331
10.1.1 Structure of Digital Signal Processing System ..... 331
10.1.2 Structure and Operation of Nontracking MTI ........ 332
10.1.3 MTI as Queuing System ............................. 335
10.2 Analysis of "n - 1 - 1" MTI System ....................... 339
10.2.1 Required Number of Memory Channels ................ 339
10.2.2 Performance Analysis of Detector-Selector ......... 340
10.2.3 Analysis of MTI Characteristics ................... 343
10.3 Analysis of "и - n - 1" MTI System ....................... 344
10.4 Analysis of "n - m - 1" MTI System ....................... 345
10.5 Comparative Analysis of Target Tracking Systems .......... 347
10.6 Summary and Discussion ................................... 349
References .................................................... 349
PART III Stochastic Processes Measuring in Radar Systems
Chapter 11 Main Statements of Statistical Estimation Theory ... 353
11.1 Main Definitions and Problem Statement ................... 353
11.2 Point Estimate and Its Properties ........................ 356
11.3 Effective Estimations .................................... 358
11.4 Loss Function and Average Risk ........................... 359
11.5 Bayesian Estimates for Various Loss Functions ............ 362
11.5.1 Simple Loss Function .............................. 363
11.5.2 Linear Module Loss Function ....................... 364
11.5.3 Quadratic Loss Function ........................... 365
11.5.4 Rectangle Loss Function ........................... 366
11.6 Summary and Discussion ................................... 366
References .................................................... 368
Chapter 12 Estimation of Mathematical Expectation ............. 369
12.1 Conditional Functional ................................... 369
12.2 Maximum Likelihood Estimate of Mathematical Expectation .. 373
12.3 Bayesian Estimate of Mathematical Expectation:
Quadratic Loss Function .................................. 381
12.3.1 Low Signal-to-Noise Ratio (p2 << 1) ............... 383
12.3.2 High Signal-to-Noise Ratio (p2 >> 1) .............. 385
12.4 Applied Approaches to Estimate the Mathematical
Expectation .............................................. 386
12.5 Estimate of Mathematical Expectation at Stochastic
Process Sampling ......................................... 397
12.6 Mathematical Expectation Estimate under Stochastic
Process Amplitude Quantization ........................... 408
12.7 Optimal Estimate of Varying Mathematical Expectation of
Gaussian Stochastic Process .............................. 413
12.8 Varying Mathematical Expectation Estimate under
Stochastic Process Averaging in Time ..................... 422
12.9 Estimate of Mathematical Expectation by Iterative
Methods .................................................. 427
12.10 Estimate of Mathematical Expectation with Unknown
Period .................................................. 430
12.11 Summary and Discussion .................................. 436
References .................................................... 439
Chapter 13 Estimation of Stochastic Process Variance .......... 441
13.1 Optimal Variance Estimate of Gaussian Stochastic
Process .................................................. 441
13.2 Stochastic Process Variance Estimate under Averaging in
Time ..................................................... 449
13.3 Errors under Stochastic Process Variance Estimate ........ 455
13.4 Estimate of Time-Varying Stochastic Process Variance ..... 460
13.5 Measurement of Stochastic Process Variance in Noise ...... 468
13.5.1 Compensation Method of Variance Measurement ....... 468
13.5.2 Method of Comparison .............................. 473
13.5.3 Correlation Method of Variance Measurement ........ 476
13.5.4 Modulation Method of Variance Measurement ......... 478
13.6 Summary and Discussion ................................... 484
References .................................................... 486
Chapter 14 Estimation of Probability Distribution and
Density Functions of Stochastic Process ....................... 487
14.1 Main Estimation Regularities ............................. 487
14.2 Characteristics of Probability Distribution Function
Estimate ................................................. 491
14.3 Variance of Probability Distribution Function Estimate ... 495
14.3.1 Gaussian Stochastic Process ....................... 495
14.3.2 Rayleigh Stochastic Process ....................... 499
14.4 Characteristics of the Probability Density Function
Estimate ................................................. 504
14.5 Probability Density Function Estimate Based on
Expansion in Series Coefficient Estimations .............. 509
14.6 Measurers of Probability Distribution and Density
Functions: Design Principles ............................. 514
14.7 Summary and Discussion ................................... 520
References .................................................... 521
Chapter 15 Estimate of Stochastic Process Frequency-Time
Parameters .................................................... 523
15.1 Estimate of Correlation Function ......................... 523
15.2 Correlation Function Estimation Based on Its Expansion
in Series ................................................ 531
15.3 Optimal Estimation of Gaussian Stochastic Process
Correlation Function Parameter ........................... 539
15.4 Correlation Function Estimation Methods Based on Other
Principles ............................................... 554
15.5 Spectral Density Estimate of Stationary Stochastic
Process .................................................. 561
15.6 Estimate of Stochastic Process Spike Parameters .......... 570
15.6.1 Estimation of Spike Mean .......................... 571
15.6.2 Estimation of Average Spike Duration and Average
Interval between Spikes ........................... 575
15.7 Mean-Square Frequency Estimate of Spectral Density ....... 579
15.8 Summary and Discussion ................................... 581
References .................................................... 582
Notation Index ................................................ 583
Index ......................................................... 597
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