Index
A
Acquisition, 115
Adaptive DGD chaotic pulse interference, 86
closed loop system, 87
flow chart, 85
noise pdf, 85
normalized factor, 87
signal detection algorithms, 84
total variance, 6
Adaptive filtering algorithms
Bayesian approach
Cartesian coordinates, 187–189
random process, 186
mixed coordinate systems implementation
azimuth coordinate vs number of measurements, 185
correlation matrix, 183
joint filtering, 184
matrix filter gain, 184
recurrent filter, 182
simplified filtering procedure, 185
spherical-local Cartesian transformation, 181–182
principles of first approach, 180
second approach, 181
state equation, 179
third approach, 181
Adaptive-nonparametric DGD, 91–93
Adaptive signal detection algorithms, 84
Adaptive threshold tuning, 91
Additional target searching, 211
Addressness, 274
Adjacency matrix, 243
Adjustment operation, 277
Algorithm graph flowchart
equivalent branches union, 244–245
final graph, 245
finite oriented graph, 243
subgraphs, 244
union of algorithms into blocks, 245
Analog-to-digital converter (ADC) dynamical and statical errors, 30–31
principles, 25
reliability, 32
sampling process
capacity digit quantization, 30
envelope, 28
instantaneous sampling, 25
phase detector, 27
phase-manipulated pulse signal, 29
quantizers, 29
Angular coordinate estimation algorithms discrete radar antenna scanning
fixed positions, 100
likelihood function, 101
signal and noise parameters, 102
Doppler frequency measurer, 103–105
uniform radar antenna scanning
block diagram, 97
discrete weight function, 96
maximal likelihood ratio criterion, 95
operations, 97
target return pulse train, 95–96
type of, 98
variance, 99
Antenna, 201
Antiaircraft and missile defense system
averted harm, 7
elements of, 6
emplacement of, 8
error variance, 8
QoS indices, 11
Automated complex radar systems, 13–15
Automatic radar systems, 309
Automatic target range tracking, 116–117
Autotracking
character of states and transitions, 140
false target range tracks, 141
gating cycle and indication, 140
graph with random transitions, 140–141
logical block diagram, 139
principles, 139
solved problems, 138
united algorithm, 142
Average duration of spike, 571, 575–578
Average interval between spikes, 571, 575–578
B
Bandwidth, 202
Bayes estimates
conditional dispersion, 382
definition, 381
description, 361
high signal-to-noise ratio, 385–386
linear module loss function, 364
low signal-to-noise ratio, 383–385
normalized signal and noise components, 383
posteriori pdf, 381
quadratic loss function, 365–366
rectangle loss function, 366
unconditional dispersion, 382
Bayes risk, 361
Beacon tracking, 149
C
Centered Gaussian stochastic process, 370
Central computer system structure, 314–315
Clutter, 201
Coherent signal preprocessing subsystem
design and construction, 315
envelope amplitudes, 318
nonrecursive smoothing filter, 317
operations, 315
structure, 316
timing diagram, FFT processors, 318
VLSI, 316
Compensation method
of correlation function measurement, 554
of variance measurement, 468–473
Complex algorithm computational process
algorithm graph flowchart
equivalent branches union, 244–245
final graph, 245
finite oriented graph, 243
subgraphs, 244
union of algorithms into blocks, 245
custom-designed hardware, 239–240
digital receiver front end, 237–238
logical and matrix algorithm flowcharts
components, 242
formula-logical block diagram, 241
transition formulas, 243
parallel general-purpose computers, 238–239
paralleling of
linear recurrent filtering algorithm macro-operations, 263–265
multichannel receiver, 265–266
target autotracking system, 266
receiver front end design, 237–238
stochastic network model
digital signal reprocessing algorithm, 246
probabilities of transitions, 247
probability of target pip, 248–249
work content evaluation
digital signal reprocessing in radar system, 252–257
elementary digital signal processing algorithm, 249–250
Complex radar systems (CRSs)
abstract model, 5
antiaircraft and missile defense system
averted harm, 7
elements of, 6
emplacement of, 8
error variance, 8
QoS indices, 11
characteristics of, 3
control algorithm design (see Control subsystem)
control radar systems, 6
deliberate interference, 12
engineering designing, 3
factors, 4
firing control system, 9
information radar systems, 6
potential error, 13
quality of service, 4
radar range, 10
signal processing system
block diagram, 16
classification, 17
optimization, 18
QoS indices, 17
sequence of, 18
special-purpose computer subsystems, 19
statistical radar theory, 15
system designing, 3
Conditionally unbiased estimate, 357
Conditional risk loss function, 361–362
Conditional variances, 357
Confidence factor, 355
Controlled functions, 205
Control radar systems, 6
Control subsystem
administration, 206
classification, 204
controlled parameters, 203
directional scanning mode, 207–211
distribution of limited power resources, 206
dynamical mode, 202
external factors, 202
formalization, 203
generalized detector, 201
hierarchical structure, 205
initial conditions, 207
low-noise amplifier, 201
optimization of functional modes, 206
power amplifier, 201
power resource control
energy expenditure under accuracy, 226–228
target information processing, 223–225
radar functional operation, 206
scanning control aerial target detection and tracking, 219–222
problem statement and criteria, 213–214
single target detection, 214–215
unknown number of target detection, 215–219
Convolution, DGD
in frequency domain
directed graph, 50
discrete Fourier transform (DFT), 47
fast Fourier transform (FFT), 49
FFT-specific processor, 51
impulse response of filters, 48
interstage delay registers, 52
inverse discrete Fourier transform (IDFT), 47–48
multiplication operations, 50
in time domain
block diagram of specifically designed processor, 46
calculation process, 47
chirp modulation, 40
flowchart of, 41
in-phase and quadrature channels, 39
principle of parallelism, 44–45
read-only memory (ROM), 44
Correlation integral, 32
Counting operators, 241
Cramer–Rao lower bound, 358
CRS, See Complex radar systems (CRSs)
Cyclic way, 345
D
Data processing, 202
Deliberate interference, 12
Detection decision, 201
Determinant, 223
DFT-Convolution-IDFT, 48
DGD, See Digital generalized detector (DGD)
Digital generalized detector (DGD)
adaptive
chaotic pulse interference, 86
closed loop system, 87
flow chart, 85
noise pdf, 85
normalized factor, 87
signal detection algorithms, 84
total variance, 6
adaptive-nonparametric DGD, 91–93
autocorrelation function, 37
binary quantized target return pulse train, 74–75
convolution in frequency domain
directed graph, 50
discrete Fourier transform (DFT), 47
fast Fourier transform (FFT), 49
FFT-specific processor, 51
impulse response of filters, 48
interstage delay registers, 52
inverse discrete Fourier transform (IDFT), 47–48
multiplication operations, 50
convolution in time domain
block diagram of specifically designed processor, 46
calculation process, 47
chirp modulation, 40
flowchart of, 41
in-phase and quadrature channels, 39
principle of parallelism, 44–45
read-only memory (ROM), 44
digital detector synthesis problem
robust signal detection algorithms, 83
SNR losses, 84
target return signal, 82
flowchart, 36
methods of the sequential analysis
average numbers of tests vs number of resolution elements, 78–79
logarithm of likelihood ratio, 75
multichannel radar systems, 77–78
Neyman–Pearson detector, 77
statistic and decision-making procedure, 76
truncation procedure, 79
two-stage signal detection procedure, 80
noises, 38
SNR, 39
statistical decisions, 87
for target return pulse train, 72–74
uncorrelated interferences, 38
Digital interperiod signal processing algorithm
complex generalized algorithm
noise environment, 106
number and content of construction, 103
DGD (see Digital generalized detector (DGD))
measurers (see Digital measurers)
moving-target indication (see Moving-target indication)
Digital measurers
angular coordinate estimation
discrete radar antenna scanning, 100–103
Doppler frequency measurer, 103–105
uniform radar antenna scanning, 95–99
quality indices, 93
Digital rejector filter
coefficient of passive interference cancellation, 62–63
elliptic filter, 61
flowchart of, 60
recursive filters, 60
with variable pulse repetition frequency, 66–67
Digital signal processing
design structure
central computer system structure, 314–315
coherent and noncoherent accumulation, 311
Hemming window, 312
interference and noise map, 313
measures, 313
passive interference cancellation, 311
probability of false alarm, 312
general statements, 309
microprocessor subsystem
asynchronous communication, 281
data bus, 282
definition, 280
specifications for effective speed, 289–292
structure and elements of, 296–299
target return signals, 299–302
multicomputer subsystem
adjustment register content, 277
factors, 276
ring coupling homogeneous subsystem, 277–278
multimicroprocessor subsystem
associative memory, 279
high complexity, 279
matrix homogeneous subsystem, 278
with multidimensional inner long-distance channel, 279
RAM/ROM, 279
with single inner long-distance channel, 279
requirements for RAM size and structure, 293–295
single-computer subsystem
features, 274
memory device size, 275
reliability, 275
single-microprocessor subsystem, functioning analysis, 285–289
structure of
central computer system, 326–327
functional requirements, 325
Dirac delta function, 551
Directional scanning, 211
Discrete Fourier transform (DFT), 47
Doppler frequency measurer, 103–105
Doppler shift, 67
Duplexer, 201
Dynamical errors, 54
Dynamic range, 201
E
Economic factors, 4
Effective speed of operation, 274
Engineering designing, 3
Envelope of normalized correlation function, 551
Environment, 4
Erlang distribution, 284
Erlang formula, 339
External noise, 202
F
Facilities, 4
Federal structure, 297
FFT-Multiplication-IFFT, 51
Field programmable gate array, 239
Figure of merit, 59
Filter transfer function module, 567
Formula-logical block diagram, 241
Free running of sweep time, 211
Function of spectral window, 564
G
Gaussian stochastic process
centralized process, 413
correlation function, 417
effective spectral density 419
estimates of coefficients, 415
flowchart of optimal measurer, 416, 421
optimal variance estimation, 441–449
orthonormalized functions, 420
physical realization, 414
probability distribution function estimate
correlation interval, 497
maximal value of variance, 497–498
normalized correlation function, 499
root-mean-square deviation, 497–498
two-dimensional pdf, 495
values of coefficients, 496
statistical characteristics, 414
white noise, 418
Global digital signal processing system
MTI system
rough channel, 331
target tracking
H
Homogeneous multicomputer subsystem, 277–278
Human element, 4
Hybrid processors, 240
I
Ideal integrator, 386
Identity matrix, 196
Information radar systems, 6
Instantaneous sampling, 25
Integral Fredholm equation, 419
Integral of probability, 10
Interference, 202
Interference method of correlation function measurement, 554
Inverse discrete Fourier transforms (IDFT), 47
K
Kronecker symbol, 152
L
Laguerre polynomials, 500, 534
Latency, 239
Level of development, 4
Likelihood function, 355
Likelihood ratio, 355
Linear modulo loss function, 359–360
Local Cartesian coordinate system, 181
Logical operators, 241
description, 359
quadratic, 360
rectangle, 360
simple, 359
Low-noise amplifier, 201
M
Maclaurin series, 384
Maneuvering target track parameters
Bayesian approach
Cartesian coordinates, 187–189
random process, 186
mixed coordinate systems implementation
azimuth coordinate vs number of measurements, 185
correlation matrix, 183
joint filtering, 184
matrix filter gain, 184
recurrent filter 182
simplified filtering procedure, 185
spherical-local Cartesian transformation, 181–182
principles of
first approach, 180
second approach, 181
state equation, 179
third approach, 181
Markov model, 250
Mathematical expectation estimation
applied approaches
asymmetric inertialess signal limiter, 393–394
bias of, 394
frequency characteristics, 390
functions of p with η, 393
integration domain, 387
measurement instant vs instant of appearance, 389
normalized correlation functions, 392
normalized variance vs p, 391
one-and two-dimensional pdf, 395
optimal methods, 386
Rayleigh stochastic processes, 396–397
RC filter time constant, 390
relative increase in variance, 391
sign-changing normalized correlation function, 387
smoothing circuit, 388
symmetric inertialess signal limiter, 393–394
variance of, 386
white noise, 389
conditional functional
centered Gaussian stochastic process, 369
correlation interval, 371
inverse Fourier transform, 372
noise component, 373
white noise, 364
Gaussian stochastic process
centralized process, 413
correlation function, 417
effective spectral density, 419
estimates of coefficients, 415
flowchart of optimal measurer, 416, 421
orthonormalized functions, 420
physical realization, 414
statistical characteristics, 414
white noise, 418
iterative methods
flowchart of measurer, 428
ratio of variance, 429
recurrent procedures, 427
maximum likelihood estimate
conditional bias and dispersion, 379
conditional pdf, 378
integral Wiener–Hopf equation, 376
optimal device structure, 374
unconditional bias and dispersion, 380
variance of, 377
weight integration, 375
quadratic loss function
conditional dispersion, 382
definition, 381
high signal-to-noise ratio, 385–386
low signal-to-noise ratio, 383–385
normalized signal and noise components 383
posteriori pdf, 381
unconditional dispersion, 382
stochastic process amplitude quantization
conditional bias, 410
correlation function, 412
inertialess element, 409
limiting case, 413
rectangular function, 409
staircase characteristics, 408–409
transducer, 410
unconditional bias, 411
stochastic process averaging in time
bias and mutual correlation functions, 426
condition, 425
correlation interval 424
effective spectral density, 427
nonstationary processes, 423
single realization, 422
stochastic process sampling
conditional and unconditional moment 407
conditional N-dimensional pdf, 397
correlation matrix, 399
determinant, 400
domain of indices, 402
equidistributed estimate, 402
limiting case, 408
measurement method, 404
multidimensional likelihood function, 398
normalized variance vs number of samples, 400–401
optimal and equidistributed estimates, 403
random variable sequence, 405
structural diagram of measurer, 405–406
weight coefficients, 398
with unknown period
adaptation process, 436
adaptive filter flowcharts, 430
block diagram of computation algorithm, 431–432
central moment, 435
covariance function, 432
harmonic component amplitude, 435
periodical function, 431
stationary mode, 434
weight coefficient, 433
Mathematical models, 5
Matrix homogeneous multimicroprocessor subsystem, 278
Maximum maximorum, 363
Mean-square frequency estimate, 579–581
Method with zero instant, 474
Microprocessor speed of operation, 274
Microprocessor subsystem
asynchronous communication, 281
coherent signal preprocessing subsystem
design and construction, 315
envelope amplitudes, 318
nonrecursive smoothing filter, 317
operations, 315
structure, 316
timing diagram, FFT processors, 318
VLSI, 316
data bus, 282
definition, 280
groups, 296
high-performance centralized subsystem, 299–301
internal and external softwares, 297
noncoherent signal preprocessing
problems content and characteristics, 296
programmable signal subsystem, 301–302
specifications for effective speed, 289–292
types of, 297
Minimax estimate, 362
Minimax risk, 362
Modeling, 5
Moving-target indication
advantages, 57
definition, 57
digital rejector filter
coefficient of passive interference cancellation, 62–63
elliptic filter, 61
flowchart of, 60
recursive filters 60
with variable pulse repetition frequency, 66–67
efficiency indices, 59
flowchart of two-channel, 58–59
passive interferences, 59
Moving target indicator (MTI) system
n–1–1 analysis
detector–selector performance analysis, 340–343
memory channels required, 339–340
MTI system, See Moving target indicator (MTI) system
Multicomputer subsystem
adjustment register content, 277
factors, 276
ring coupling homogeneous subsystem, 277–278
Multidimensional likelihood function, 441
Multimicroprocessor subsystem
associative memory, 279
high complexity, 279
matrix homogeneous subsystem, 278
with multidimensional inner long-distance channel, 279
RAM/ROM, 279
with single inner long-distance channel, 279
Mutual correlation function estimate, 528–529
N
Neyman–Pearson detector, 80
Nontracking moving target indicator system
binary signal processing, 332–333
description, 332
detection–selection problem, 334
two-dimensional likelihood ratio surface, 333
Normalized noise component, 383
Normalized noise functions, 545
Normalized signal component, 383
Number representation capacity, 274
Number representation form, 274
O
Off-line mode, 276
One-dimensional probability distribution function, 487
Operation of generalized conditional jump, 277
Operation of generalized unconditional jump, 277
Operation of information exchange, 277
Optimal scanning control, 220
P
Paralleling of computational process
linear recurrent filtering algorithm macro-operations, 263–265
multichannel receiver, 265–266
multilevel graph
adjacency matrix elements, 259–260
dimensions of matrices and vectors, 259
distribution of tops along levels, 261–262
graph tops distribution, schematic illustration, 258
linear recurrent filtering, 259
quantitative characteristics, 258
schematic illustration, 258
serial–parallel operation 257
tops of initial graph, 261
transformations, 262
organization of paralleling, 266–267
target autotracking system, 266
Phase detector, 27
Point estimates
characteristics, 356
conditionally unbiased estimate, 357
conditional variances, 357
description, 356
properties, 357
unconditional estimate, 356–357
unconditional mutual correlation function, 357
Posteriori risk, 362
Power amplifier, 201
Power resource control
energy expenditure under accuracy, 226–228
target information processing, 223–225
Probability density function estimate
characteristics
dependences vs normalized interval, 508
discrete stochastic process, 507
Gaussian and Rayleigh stochastic process, 506
normalized errors, 509
normalized observation interval, 506
variance of, 507
definition, 488
design principles
computation algorithm, 516
measurer, 515
direct measurement, 489
expansion in series coefficient estimations
analogous way, 514
coefficients of, 510
distribution histogram, 513
independent random variables, 512
measurer, 511
orthogonal functions, 509
root-mean-square deviation, 510
Probability distribution function estimate
approximation accuracy, 487
characteristics
correlation function 492
mathematical expectation and dispersion, 495
observation time period 494
two-dimensional pdf, 492
unbiased, 493
variance of, 494
computation method, 490
definition, 487
design principles
argument estimate computation, 518
computing algorithm, 520
measurer, 519
transformation, 517
direct measurement, 489
Gaussian stochastic process
correlation interval, 497
maximal value of variance, 497–498
normalized correlation function, 499
root-mean-square deviation, 497–498
two-dimensional pdf, 495
values of coefficients, 496
nonlinear transformation 491
Rayleigh stochastic process
coefficients of, 502
correlation function of, 501
maximal value of variance, 503
normalized correlation function, 502, 504
observation interval, 503
orthogonal Laguerre polynomials, 500
root-mean-square deviation, 503
two-dimensional pdf, 499
variance of, 502
Programmable signal microprocessor subsystem, 301–302
Q
Quadratic loss function, 360
Quadratic transformer, 455
Quadrator, See Quadratic transformer
Quality of service (QoS)
multiphase queuing system, 339
target tracking systems, 347
Quantizers, 29
Queuing system
average request queuing waiting time vs the request queuing priorities, 288
Erlang distribution, 284
flow chart, 285
interference flux, 283
limited waiting time, 284
Poisson flow, 283
quality parameters, 286
radar coverage, 282
regulations, 287
total loading factor, 286
Queuing system with the limited queue, 284
R
Radar control, 202
Radar measurers, 331
Radar signal preprocessing system, 17
Radar signal processing system
block diagram, 16
classification, 17
optimization, 18
QoS indices, 17
sequence of, 18
special-purpose computer subsystems, 19
statistical radar theory, 15
Radar signal reprocessing
QoS indices, 17
Rayleigh stochastic process
probability distribution function estimate
coefficients of, 502
correlation function of, 501
maximal value of variance, 503
normalized correlation function, 502, 504
observation interval, 503
orthogonal Laguerre polynomials, 500
root-mean-square deviation, 503
two-dimensional pdf, 499
variance of, 502
Rectangle loss function, 360
Recurrent filtering algorithms
formula flowchart
Gaussian distribution, 172
sequential filtering algorithm, 174–177
stabilization methods
artificial aging, 179
extrapolation errors, 178
gain lower bound, 179
smoothing method, 177
Reliability, 32
S
Sampling process
capacity digit quantization, 30
envelope, 28
instantaneous sampling, 25
phase detector, 27
phase-manipulated pulse signal, 29
quantizers, 29
Scanning control
aerial target detection and tracking, 219–222
problem statement and criteria, 213–214
single target detection, 214–215
unknown number of target detection, 215–219
Signal processor, 201
Signal-to-noise ratio (SNR), 545–546
Sign methods of correlation function measurement, 559
Simple loss function, 359
Simplest Poisson flow, 283
Simulation models, 5
Single-computer subsystem
features, 274
memory device size, 275
reliability, 275
Single-microprocessor queueing system, 285–289
Skin tracking, 149
SNR, See Signal-to-noise ratio (SNR)
Statistical estimation theory
conditional probabilities, 354
Cramer–Rao lower bound, 358
effective unbiased estimate, 358
estimate criteria, 353
likelihood function, 355
likelihood ratio, 355
loss function
description, 359
quadratic, 360
rectangle, 360
simple, 359
point estimate
characteristics, 356
conditionally unbiased estimate, 357
conditional variances, 357
description, 356
properties, 357
unconditional estimate, 356–357
unconditional mutual correlation function, 357
posteriori pdf formula, 354
Stochastic network model
digital signal reprocessing algorithm, 246
probabilities of transitions, 247
probability of target pip, 248–249
Stochastic process amplitude quantization
conditional bias, 410
correlation function, 412
inertialess element, 409
limiting case, 413
rectangular function, 409
staircase characteristics, 408–409
transducer, 410
unconditional bias, 411
Stochastic process averaging in time
bias and mutual correlation functions, 426
condition, 425
correlation interval, 424
effective spectral density, 427
nonstationary processes, 423
single realization, 422
Stochastic process estimation
probability density function (see Probability density function estimate)
probability distribution function (see Probability distribution function estimate)
Stochastic process frequency-time parameters
average spike duration and interval between spikes
mathematical expectation, 577
measurer flowchart, 576
normalized correlation function, 578
normalized squared deviation, 576
correlation function
approximation error, 535
compensation method, 556
correlator, 524
discrete step, 524
exponential correlation function, 526
Gaussian stochastic process, 527
mathematical expectation, 537–538
mpulse characteristic estimate, 530
multichannel correlator, 525
mutual correlation function, 528–529
normalized correlation function, 557–558
normalized orthogonal functions, 531–532
one-channel measurer, 534
orthogonal function, 533
orthogonal Laguerre polynomials, 534
realization process, 528
sequential measurement, 524–525
spectral density, 523
straight-line interpolation, 524
mean-square frequency estimate, of spectral density, 579–581
optimal estimate
bias and variance of, 549, 552
correlation matrix, 553
effective bandwidth of spectral density, 549, 551
Fourier transforms, 542, 552–553
infinite limits of integration, 541
likelihood functional ratio, 540, 544–545, 552
maximum likelihood ratio, 543
measurer flowchart, 542
narrowband stochastic process, 550–551
normalized signal and noise functions, 545–546
observation time interval, 550
random error, 547
root-mean-square deviation, 553–554
signal and noise, 541
signal-to-noise ratio, 545–546
spectral representation, 542
spectral density estimate
correlation function of, 563
dispersion of, 570
filtering method, 567
Fourier transform of correlation function, 561
mathematical expectation of, 562
measurer flowchart, 568
observation time interval, 565
spectrum frequency shift measurement, 568
variance of, 564
spike mean estimation
mathematical expectation, 572
mean-square frequency, 579–581
normalized squared deviation, 574–575
normalized variance 574
observation time interval, 571
probability distribution functions, 573
transformation process, 570
Stochastic process sampling
conditional and unconditional moment, 407
conditional N-dimensional pdf, 397
correlation matrix, 399
determinant, 400
domain of indices, 402
equidistributed estimate, 402
limiting case, 408
measurement method, 404
multidimensional likelihood function, 398
normalized variance vs number of samples, 400–401
optimal and equidistributed estimates, 403
random variable sequence, 405
structural diagram of measurer, 405–406
weight coefficients, 398
Stochastic process variance estimation
averaging in time
iterative variance estimate, 455
mathematical expectation, 451
measurer operating in accordance, 450
observation time interval, 452–453
optimal weight function, 450
transformations, 453
unbiased variance estimate, 455
uncorrelated and correlated samples, 452
comparison method
deterministic harmonic signal 475
measurer flowchart, 473
reference signal, 474
squarer inputs signal, 473–474
time interval of observation, 475
compensation method
additional random errors, 471
flowchart of, 468
integrator output, 473
radiometer sensitivity, 472
time interval of observation, 470
variance of variance, 470, 472
zero mathematical expectation and correlation function, 469
correlation method
additional errors, 478
flowchart of, 476
integrator output signal, 476
quadratic transformation 478
sensitivity of, 478
time interval of observation, 477
errors
bias of variance estimate, 456, 460
Gaussian stochastic process, 456
measurer, additional signals based, 458
squaring operation avoidance, 456–457
transformation, 456
zero mathematical expectations, 457–458
modulation method
amplifier input signal, 479 482
correlation interval, 481
deterministic harmonic signal, 484
ideal integrator output signal, 482
quadrator output, 480
reference process, 479
switching function frequency, 480
time interval of observation, 481
total realization, 479
variance estimate, 483
optimal variance estimate
additive stochastic process, 443–444
computing the variation, 445
conditional multidimensional pdf, 441
correlation function, 444, 447
likelihood function, 446
mathematical expectation, 442
multidimensional likelihood function, 441
multidimensional sampling 447
normalized correlation function, 448
power spectral density, 444
signal processing in noise, 443–444
variations and mathematical expectations, 448–449
centralized stochastic process, 462
coefficient estimations, 466
correlation function, 464
mathematical expectation, 461
measurer of variance 465
N independent realizations, 460
orthonormalized functions, 467
quadratic error, 463
single realization, 461
Subsystems, 3
Switching function frequency, 480
System designing, 3
T
Target characteristics, 202
Target maneuver intensity, 152
Target pip gating
algorithm of indication, 122–125
distribution and binding, 125–128
initial parameters, 118
shape selection and dimensions, 119–122
Target range autotracking, See Autotracking
Target range detection, See Target range tracking
Target range tracking
acquisition, 115
characteristics, 129
circuitry, 115
clutter number, 117
coordinate system, 117
operations, 118
parameters, 117
prerequisites, 129
statistical analysis 2/m + 1/n algorithms
false target range detection, 129–135
true target range detection, 135–138
target pip gating
algorithm of indication, 122–125
distribution and binding, 125–128
initial parameters, 118
shape selection and dimensions, 119–122
Target tracking
Target track model
errors, 154
filtered target parameters, 150
function, 153
no maneuvering targets, 153
target maneuver intensity, 152
undisturbed parameters, 151
united dynamic model, 155
Target track parameters
adaptive filtering algorithms
mixed coordinate systems implementation, 181–185
clutter number, 149
conditions, 150
extrapolation algorithm, 166–168
in filtering subsystems
stochastic parameters, 155–156
measure error, 157
multiobject tracking radar (MOTR), 149
parameter estimation
dynamic errors, polar coordinate system, 168–170
error correlation matrix, 159–162
maximal likelihood criterion, 157–158
second-order polynomial, 162–166
skin tracking, 149
target noise, 150
undistorted polynomial target
optimal filtering algorithm formula flowchart, 170–174
sequential filtering algorithm, 174–177
stabilization methods, 177–179
Technology refresh cycle, 240
Three-phase queuing systems, 336
Time-domain multiplexing, 240
Transmitter, 201
Two-dimensional probability distribution function, 492
U
Unconditional estimate, 356–357
Unconditional mutual correlation function, 357
Unconditional risk loss function, 361–362
V
Variance of a priori distribution, 385
Variance of variance estimate, 446
Verilog, 240
W
Weight window function, 105
Widrow–Hopf algorithm, 431
Wilcoxon statistic, 90
Z
Zolotaryov–Cauer filter, 61