Index
A
Acoustic signal processing
chemical sensor arrays, 943
Adaptive ATC strategy, 394
algorithms employing
spatial reference, 900
temporal reference, 901
basic principles, 508
blind algorithms, 902
general-rank source, 513
gradient adaptive beamforming algorithms, 513
hybrid beamformers, 901
MVDR beamforming with data covariance matrix, 512
optimal SINR, 512
projection adaptive beamforming methods, 515
reduced complexity approaches to adaptive beamforming, 516
sample matrix inversion adaptive beamformer, 514
wideband adaptive beamforming, 519
Adaptive broadband beamforming, 584
Adaptive CTA strategy, 393
Adaptive diffusion strategies with smoothing mechanisms, 415
Adapt-then-combine (ATC) diffusion strategy, 353
AIC. See Akaike information criterion (AIC)
Airborne fast vehicles, 278
Airborne slow vehicles, 280
Algorithms using tensor-based subspace estimates, 698
R-D NC standard tensor-ESPRIT, 700
R-D unitary tensor-ESPRIT, 699
Ambiguity function, 77
Angle-Doppler spectra, 870
Aperture theory, 556
GNSS-specific signal models, 906
structured spatial signatures and spatially white noise, 905
structured spatial signatures and unknown spatial correlation, 905
unstructured spatial signatures and spatially white noise, 905
unstructured spatial signatures and unknown spatial correlation, 905
robust beamforming using, 848
Array geometries, 557
Array interpolation technique, 836
Array nonidealities, 825
array elements’ beampatterns and positions, 826
cross-polarization effects, 827
mutual coupling, 825
narrowband signal model, 828
nonlinear elements, effects of, 829
receiver front-end architectures, 828
Array processing
beam forming and signal detection, 480
adaptive beamforming, 482
signal detection, 485
spatial filter design, 480
direction-of-arrival estimation, 486
beamforming methods, 487
modeling errors and array calibration, 492
parametric methods, 489
subspace methods, 488
geometric data model, 465
ideal data model, 466
non-ideal data models, 470
wave propagation, 465
non-Coherent array applications, 493
microwave and ultrasound imaging, 497
sensor networks, source localization in, 497
spread sources, 493
time series modeling, 495
spatial filtering and beam patterns, 471
one-dimensional arrays, 472
spatial filtering, 471
two-dimensional arrays, 475
wideband array response, 477
Array signal processing
adaptive and robust beamforming, 458
applications of, 460
array processing, 458
biomedical applications, 917
broadband beamforming and optimization, 458
classification of techniques, 821
methods and algorithms, 458
of nonstationary signals, 459
performance bounds and statistical analysis of, 459
examples, 846
face of non idealities, 460
history, 457
ideal array signal models, 821
nonstationary signals, 459
outlook, 461
polynomial rooting techniques, 849
robust beamforming using array calibration, 848
source localization and tracking, 460
special array structures, subspace methods and exploitation of, 459
wireless communications, 907
Array steering vectors, 820
Astronomical phased array feeds, 885
beamformer calculation, 888
calibration, 888
radio camera results, 889
Asymptotic analysis
and central limit theorem, 313
and parametric models, 315
Asymptotic distribution
estimated DOA, 736
high-order algorithms, 750
maximum likelihood algorithms, 738
robustness of algorithms, 747
subspace-based algorithms, 745
of statistics, 724
Asymptotic regime, 194
Attenuation, 803
Autoregressive (AR) modeling, 328
cooperative adaptation through diffusion, 334
linear model, 328
non-cooperative adaptive solution, 331
non-cooperative mean-square-error solution, 330
B
Bandwidth, 876
Bayesian computational methods, 5
computational methods, 161
expectation-maximization (EM), for MAP estimation, 162
Markov chain Monte Carlo (MCMC), 163
parameter estimation, 143
Bayesian inference, 147
Bayesian model averaging, 161
linear Gaussian model, 144
maximum likelihood (ML) estimation, 146
model uncertainty and Bayesian decision theory, 158
model uncertainty, structures for, 161
particle filtering and auxiliary sampling, 169
marginalized particle filters, 171
particle filters, 177
probability densities and integrals, 178
gamma density, 180
inverse Wishart distribution, 182
inverted-gamma distribution, 180
multivariate Gaussian, 178
normal-inverted-gamma distribution, 181
univariate Gaussian, 178
Wishart distribution, 181
state-space models and sequential inference, 164
linear Gaussian state-space models, 164
prediction error decomposition, 166
sequential Monte Carlo (SMC), 167
Bayesian i.i.d. setting, 217
Bayesian inference, 147
covariance matrices, priors on, 157
G-prior, 157
hyperparameters and marginalization, of unwanted parameters, 152
linear Gaussian model, hyperparameters for, 153
linear Gaussian model, parameters in, 151
Marginal likelihood, 152
normal-inverted-gamma prior, 154
posterior inference and Bayesian cost functions, 149
Bayesian information criterion (BIC), 14
Bayesian model averaging, 161
Bayesian quickest change detection, 217
Beamformer architecture, 887
Beam forming and signal detection, 480
Beamforming methods, 487
adaptive beamforming algorithms, 899
deterministic, 903
Beamspace processing, 638
BIC. See Bayesian information criterion (BIC)
Binary hypothesis testing problem, 188
Binary RSS measurements, 289
Biomedical applications, array signal processing, 917
electroencephalography (EEG), 918
magnetoencephalography (MEG) signal processing, 918
ultrasound imaging, 918
Biomedical signal analysis, 137
Blackman window, 32
Block maximum norm, 435
Bootstrap methods, 12
Bootstrapping, 14
Born-Jordan distribution, 83
Broadband beamformer, 574
Broadband beamforming and optimization
adaptive broadband beamforming, 584
common signal modeling, 584
frequency domain, generalized sidelobe canceler in, 589
frequency domain Wiener filter, 591
generalized sidelobe canceler (GSC), 587
LCMV in frequency domain, 586
linearly constrained minimum variance (LCMV) beamforming, 584
Wiener filter, 590
design in element space, 558
broadband beamformer, 574
Chebyshev design, 563
design examples, 568
model and robust formulation, 563
robust Chebyshev design, 567
robust total least squares design, 567
robust WLS design, 566
steerable broadband beamformer, 571
total least squares design and Eigen-filters, 562
weighted least square (WLS) design, 561
design using wave equation, 574
design examples, 582
spherical broadband beamformer, 581
wave equation, 579
environment and channel modeling, 556
aperture theory, 556
array geometries, 557
examples for optimal beamformers, 593
optimal near-field signal-to-noise plus interference beamformer (SNIB), 591
frequency domain formulation, 593
time domain formulation, 591
Butterworth distribution, 83
C
Capon beamformer. See Minimum variance distortionless response (MVDR) beamformer
Car engine signal analysis, 137
Cellular phones, 285
binary RSS measurements, 289
continuous RSS measurements, 286
Chair-Varshney fusion rule, 200
Channel aware distributed detection, 197
Chebyshev design, 563
Chemical sensor arrays, 943
Closely spaced sources, resolution of, 755
mean null spectra, angular resolution limit, 755
Cognitive radio, 250
Cohen class of distributions, 80
auto-terms form, 87
reduced interference distributions, 83
Coherent processing interval (CPI), 865
Collaborative spectral sensing, 341
Combination weights, 396
Combine-then-adapt (CTA) diffusion strategy, 355
Common signal modeling, 584
Complex argument distribution, 114
Computational methods, 161
Computer network security, 250
Conditional independence assumption, 190
asymptotic regime, 194
Bayesian formulation, 190
decision fusion problem, 192
Neyman-Pearson formulation, 191
Consensus recursion, 442
Consensus strategies, comparison with, 442
Constant combination weights, 397
Constrained Cramér-Rao bound (CCRB), 308
Constrained maximum-likelihood estimation (CMLE), 310
Continuous RSS measurements, 286
Controlled Reception Pattern Antennas (CRPAs), 898
Conventional beamformer, 605
Convergence behavior, 368
Convergence in mean, 409
Cooperative adaptation through diffusion, 334
Coordinated Multipoint transmission (CoMP), 913
Copula theory, 199
Covariance matching estimation methods, 626
Covariance matrices, priors on, 157
CPI. See Coherent processing interval
bias-informed, 301
Gaussian deterministic case, 732
Gaussian stochastic case, 730
general CRB expression, 301
on parameter estimation, 299
properties, 302
transformations, 301
CRB. See Cramér-Rao bounds (CRB)
CRLB. See Cramer-Rao Lower Bound (CRLB)
Cross-polarization discrimination (XPD), 827
Cross-polarization effects, 827
Cross-validation (CV), 12
CRPAs. See Controlled Reception Pattern Antennas
CuSum procedure, 211
CV. See Cross-validation (CV)
D
Data and beamforming models, 504
narrowband case, 505
general-rank source, 506
point source, 505
wideband case, 507
Data association problem, 802
Data-driven techniques, 834
array interpolation technique, 836
Data-efficient quickest change detection, 244
notation, 654
special array structures, 657
dynamical models, 273
inertial models, 273
marginalization of speed, 273
odometric models, 272
Decision fusion problem, 192
DE-Shiryaev algorithm, 245
Design using wave equation, 574
Diagonally loaded SMI beamformer, 522
Diffusion adaptation over networks, 5
convergence in mean, 379
data model, 374
error recursions, 377
mean-square performance, of individual nodes, 387
mean-square stability, 381
network mean-square performance, 386
performance measures, 375
transient mean-square performance, 390
uniform data profile, 389
Block maximum norm, 435
combination weights, 396
adaptive combination weights, 401
constant combination weights, 397
optimizing combination weights, 398
consensus recursion, 442
consensus strategies, comparison with, 442
cooperative strategies, 391
ATC and CTA strategies, 392
information exchange, 393
non-cooperative strategy, 394
distributed optimization via diffusion strategies, 345
adapt-then-combine (ATC) diffusion strategy, 353
combine-then-adapt (CTA) diffusion strategy, 355
global cost to neighborhood costs, 347
properties of diffusion strategies, 357
steepest-descent iterations, 351
error recursion, 443
extensions and variations, 414
adaptive diffusion strategies with smoothing mechanisms, 415
diffusion distributed optimization, 426
diffusion Kalman filtering, 423
diffusion recursive least-squares, 419
graph laplacian and network connectivity, 430
mean-square-error estimation, 327
autoregressive modeling, 328
collaborative spectral sensing, 341
tapped-delay-line models, 334
target localization, 336
motivation, 323
cooperation among agents, 326
networks and neighborhoods, 324
notation, 326
noisy information exchanges, 403
adaptive combination weights, 412
convergence in mean, 409
error recursion, 405
mean-square convergence, 410
noise sources over exchange links, 404
properties of Kronecker products, 430
steepest-descent diffusion strategies, 364
convergence behavior, 368
error recursions, 366
general diffusion model, 364
stochastic matrices, 433
Diffusion distributed optimization, 426
noiseless updates, 427
updates with gradient noise, 428
Diffusion Kalman filtering, 423
Diffusion recursive least-squares, 419
effect of cross-terms, 784
spatial joint-variable domain distributions, 788
time-frequency MUSIC, 780
Discrete pseudo Wigner distribution, 75
Discrete S-method, 91
Discrete STFT, signal reconstruction form, 44
Discrete wavelet transform, 927
Distributed sensor systems, 247
Distributed signal detection, 4
with dependent observations, 198
with independent observations
channel aware distributed detection, 197
conditional independence assumption, 190
energy efficient distributed detection, 197
multi-objective optimization, 197
network topologies, 194
nonparametric rules, in distributed detection, 196
DOA. See Direction of arrival (DOA)
DOA estimation methods and algorithms
background, 599
beamforming methods, 604
conventional beamformer, 605
minimum variance distortionless response (MVDR) beamformer, 606
numerical examples, 609
sparse data representation based approach, 607
beamspace processing, 638
data model, 600
frequency domain description, 601
uniqueness, 604
wave propagation, 600
distributed sources, 639
parametric methods, 617
covariance matching estimation methods, 626
implementation, 620
maximum likelihood approach, 618
numerical examples, 628
performance bound, 627
subspace fitting methods, 625
polarization sensitivity, 640
signal detection, 634
additional issues, 636
nonparametric methods, 634
parametric methods, 636
signals with known structures, 637
spatially correlated noise fields, 638
subspace methods, 610
estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, 613
MUSIC algorithm, 612
numerical examples, 616
signal coherence, 614
tracking, 637
wideband DOA estimation, 631
coherent signal subspace methods, 633
wideband maximum likelihood estimation, 632
DOF. See Degrees of freedom (DOF)
Doob’s optional stopping theorem, 213
Doppler velocity log, 282
Doubly constrained robust adaptive beamforming, 539
Dynamical models, 273
E
EADF. See Effective aperture distribution function
ECoG measurements
unified dipole model, 919
EEG and MEG signal processing, 918
unified dipole model, 919
Eigen-filters, 562
Eigenspace-based beamformer, 537
Eigenvalue beamforming using multi-rank MVDR beamformer, 541
EKF. See Extended Kalman filter
Electroencephalography (EEG) signal processing, 918
Energy efficient distributed detection, 197
Environment and channel modeling, 556
comparison with diffusion strategies, 447
convergence conditions, 443
rate of convergence, 445
ESPRIT algorithm. See Estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm
Expectation-maximization (EM) algorithm, 5
for MAP estimation, 162
Extended Invariance Principle (EXIP), 905
F
False discovery rate (FDR), 196
Far-field assumption, 601
FDR. See False discovery rate (FDR)
Filter bank STFT implementation, 38
Finite impulse response digital filter, 803
Finite Impulse Response (FIR) filtering, 463
Frequency domain description, 601
general model, 602
narrow band data, 603
Frequency domain formulation, 593
Frequency domain, generalized sidelobe canceler in, 589
Frequency domain Wiener filter, 591
Frequency Shift Transmit Diversity (FSTD), 908
FSTD. See Frequency Shift Transmit Diversity
Functional analysis, 723
G
Gabor transform, 45
Gamma density, 180
Gaussian case, 311
Gaussian deterministic case, 732
Gaussian model, 5
Gaussian stochastic case, 730
Gaussian window, 32
General asymptotic Bayesian theory, 221
General asymptotic minimax theory, 237
General diffusion model, 364
Generalized CuSum algorithm, 238
Generalized weighted subspace fitting (GWSF) algorithm, 832
GeneralizedWigner Distribution (GWD), 60
Generalmaximumlikelihood theory, 16
General-rank signal model, 545
General statistical tools, DOA estimation, 723
specific algorithm, performance analysis of, 723
Geographical information system (GIS), 258
Geolocation, 6
Geolocation–maps
estimation methods, 260
extended Kalman filter, 264
nonlinear filtering, 261
nonlinear filter theory, 261
particle filter (PF), 267
unscented Kalman filter (UKF), 265
mapping in practice, 292
maps and applications, 276
airborne fast vehicles, 278
airborne slow vehicles, 280
cellular phones, 285
road-bound vehicles, 276
small migrating animals, 290
surface vessels, 283
underwater vessels, 282
motion models, 270
dead-reckoning model, 272
kinematic model, 274
theory, 259
Geometric data model, 465
Geometric triangulation, 799
Global cost to neighborhood costs, 347
beamforming, 898
Global Positioning System (GPS), 893
GLRT-based sequential hypothesis testing. See Generalized likelihood ratio test (GLRT-) based sequential hypothesis testing
GNSS. See Global Navigation Satellite Systems
G-prior, 157
Gradient adaptive beamforming algorithms, 513
Graph laplacian and network connectivity, 430
GWSF algorithm. See Generalized weighted subspace fitting algorithm
H
Hann(ing) window, 32
Heuristic approach, 9
Higher order time-frequency representations, 107
Hybrid time and frequency varying windows, 41
I
Ideal array signal models, 821
Ideal data model, 466
i.i.d. model with geometric prior, 225
Inertial models, 273
Information and coding theory based methods, 17
Inner interferences in Wigner distribution, 72
Instantaneous bandwidth, 65
Instantaneous frequency (IF)
distribution concentrated, 61
interpretation, 48
Inverse Wishart distribution, 182
Inverted-gamma distribution, 180
K
Kaiser window, 32
Kalman filter, 814
nonlinear observation model, 815
prediction phase, 814
update phase, 814
Kernel constraint, 82
Kernel decomposition method, 88
Kernel transformations, 85
Kinematic model, 274
K-L divergence. See Kullback-Leibler (K-L) divergence
Kronecker products, properties of, 430
L
LCMV in frequency domain, 586
Leaky Integrate-and-Fire model, 250
Least squares estimation, 316
Linear coordinate transforms, of Wigner distribution, 69
Linear Gaussian model, 144
hyperparameters for, 153
parameters in, 151
Linear Gaussian state-space models, 164
Linearly constrained minimum variance (LCMV) beamforming, 584
Linear model, 328
Linear signal transforms, 28
Local polynomial Fourier transform (LPFT), 50
Log posterior density, 14
Look direction mismatch (pointing error) problem, 523
Lorden’s problem, 230
Low system temperatures, 876
LSMI adaptive beamformers, 538
L-statistics in time-frequency, 131
L-Wigner distribution realization, 117
M
Magnetoencephalography (MEG) signal processing, 918
Marginalization of speed, 275
Marginalized particle filters, 171
Marginal likelihood, 152
calculation of, 159
Markov transition matrix, 176
Martingales, 212
Matched field processing (MFP), 935
Mathematical preliminaries, 212
Matrix-based subspace estimation, 667
Matrix perturbations, 307
Maximum likelihood algorithms, 738
asymptotic properties, 739
Maximum likelihood approach, 618
deterministic maximum likelihood, 618
stochastic maximum likelihood, 619
Maximum likelihood (ML) estimation, 146
Maximum likelihood estimation (MLE), 303
MCMC. See Markov chain Monte Carlo (MCMC)
MDL. See Minimum description length (MDL)
Mean-square convergence, 410
Mean-square error bound, 305
Mean-square-error estimation, 327
Mean-square performance, of individual nodes, 387
Mean-square stability, 381
Microwave and ultrasound imaging, 497
MIMO. See Multiple-input multiple-output (MIMO)
Minimax algorithms, optimality properties of, 234
Minimax approach, 211
Minimax quickest change detection, 228
Mixture Kalman filter, 171
ML estimation. See Maximum likelihood (ML) estimation
MODE. See Method of direction of arrival estimation
Model and robust formulation, 563
Modeling errors and array calibration, 492
Model order selection, 6
information and coding theory based methods, 17
Akaike information criterion (AIC), 17
minimum description length, 19
regression, variable selection in, 11
AIC and stepwise regression, 12
bootstrap methods, 12
cross-validation (CV), 12
statistical inference paradigms
Bayesian information criterion (BIC), 14
GLRT-based sequential hypothesis testing, 16
subspace methods, signals in, 21
Model uncertainty
and Bayesian decision theory, 158
structures for, 161
Monte Carlo method (MCM), 317
Multi-dimensional algorithms, 690
R-D NC standard ESPRIT, 696
R-D unitary ESPRIT, 691
Multi-objective optimization, 197
Multiple antennas techniques
LTE
uplink MIMO, 913
flexible transmit beampattern synthesis, 871
joint DOD/DOA estimations, 791
signal model, 790
UAV equipped with, 872
root-MUSIC, 676
unitary root-MUSIC, 677
weighted MUSIC, 675
Multiplicative and additive noise model, 310
data model, 926
multi-sensor feature extraction, 926
Multi-sensor feature extraction, 926
discrete wavelet transform, 927
principal component analysis, 927
Multi-time Wigner higher order distribution (MTWD), 110
Multivariate Gaussian, 178
MUSIC. See Multiple signal classification
MVDR beamformer. See Minimum variance distortionless response beamformer
MVDR beamforming with data covariance matrix, 512
MVDR robust adaptive beamforming design, 536
N
Network mean-square performance, 386
Networks and neighborhoods, 324
Network topologies, 194
Neuroscience, 250
Neyman-Pearson formulation, 191
Noise, 803
Noise eigenvectors, 610
Noise sources over exchange links, 404
Noise vector, 11
Noisy information exchanges, 403
adaptive combination weights, 412
convergence in mean, 409
error recursion, 405
mean-square convergence, 410
noise sources over exchange links, 404
Non-coherent array applications, 493
Non-cooperative adaptive solution, 331
Non-cooperative mean-square-error solution, 330
Non-cooperative strategy, 394
Non-Gaussian case, 311
Non-ideal data models, 470
Nonlinear filtering, 261
Nonlinear filter theory, 261
Bayes optimal filter, 261
covariance bound, 263
Kalman filter, 264
mean and covariance, 263
Non-linear least square source localization, 809
least square solution, 810
nonlinear quadratic optimization, 809
source localization using table look-up, 810
Nonlinear observation model, 815
Nonlinear renewal theory, 216
Nonparametric rules, in distributed detection, 196
Non-stationary signal analysis, 5
Non-stationary signal analysis time-frequency approach
higher order time-frequency representations, 107
signal phase derivative and distributions definitions, 112
Wigner bispectrum, 107
Wigner higher order spectra, 108
Wigner multi-time distribution, 110
linear signal transforms, 28
discrete form and realizations of STFT, 36
Gabor transform, 45
generalization, 56
local polynomial Fourier transform, 50
short-time Fourier transform, 28
stationary phase method, 46
STFT and continuous wavelet transform, 52
quadratic time-frequency distributions, 58
ambiguity function, 77
Cohen class of distributions, 80
Kernel decomposition method, 88
Rihaczek distribution, 58
S-method, 89
time-frequency, reassignment in, 99
time-frequency representations, affine class of, 104
Wigner distribution, 60
sparse signals in time-frequency, 124
compressive sensing, 131
concentration measures, 124
L-statistics in time-frequency, 131
sparse signals, 126
time-frequency analysis applications, 135
biomedical signal analysis, 137
car engine signal analysis, 137
seismic signal analysis, 137
spread spectrum systems, interference rejection in, 139
time-frequency radar signal processing, 135
time-variant filtering, 138
video sequence, velocities of moving objects, 138
watermarking, in space/spatial-frequency domain, 140
Nonstationary signals, 767
and time-frequency representations, 767
Normal-inverted-gamma distribution, 181
Normal-inverted-gamma prior, 154
Normalized maximum likelihood approach, 19
Notation, 326
Number of sources, detection of, 752
O
Odometric models, 272
One-dimensional algorithms, 674
Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), 678
root-MUSIC, 676
root-RARE, 686
unitary root-MUSIC, 677
weighted MUSIC, 675
One-dimensional arrays, 472
On-source minus off-source radiometric detection, 876
Optimal near-field signal-to-noise plus interference beamformer (SNIB), 591
Optimal SINR, 512
Optimizing combination weights, 398
Orthogonal matching pursuit, 12
P
Parallel configuration, 189
Parallel factor (PARAFAC) analysis, 652
Parameter estimations, 772
Parametric methods, 489
Parametric statistical models, 298
Parsimony, principle of, 12
Particle filtering and auxiliary sampling, 169
Path integration, 259
Performance analysis, 6
Performance analysis and bounds
asymptotic analysis and central limit theorem, 313
asymptotic analysis and parametric models, 315
Fourier transform, 315
least squares estimation, 316
asymptotic normality and MLE, 304
confidence intervals, 318
constrained Cramér-Rao bound and constrained MLE, 308
comments and properties of CCRB, 309
constrained CRB, 308
constrained MLE, 310
Cramér-Rao bound, 299
maximum likelihood estimation and CRB, 303
mean-square error bound, 305
Monte Carlo method (MCM), 317
approximate an expectation, 318
computing CRB via Monte Carlo, 318
multiplicative and non-Gaussian noise, 310
Gaussian case, 311
multiplicative and additive noise model, 310
Non-Gaussian case, 311
parametric statistical models, 298
perturbation methods, 306
matrix perturbations, 307
perturbation analysis of MLE, 308
perturbations and statistical analysis, 306
Performance bound, 627
ML methods, 627
subspace methods, 627
Performance measures, 375
Perturbation methods, 306
Phase distortion, 803
Polarization sensitivity, 640
Pollak’s problem, 231
Polynomial phase signal (PPS), 772
beamforming, 898
DOA estimation algorithms, 903
signal model, 896
Posterior inference and Bayesian cost functions, 149
Prediction error decomposition, 166
Predictor-corrector formulation, 169
Probability densities and integrals, 178
Probability distribution function (PDF), 799
Probability mass function (PMF), 815
Product higher order ambiguity function (PHAF), 124
Projection adaptive beamforming methods, 515
Pseudo and smoothed Wigner distribution, 73
Pseudo quantum signal representation, 64
Q
Quadratic time-frequency distributions, 58
Quickest change detection, 4
applications of, 250
Bayesian quickest change detection, 217
Bayesian i.i.d. setting, 217
general asymptotic Bayesian theory, 221
independent and identically distributed model with geometric prior, 225
mathematical preliminaries, 212
martingales, 212
renewal and nonlinear renewal theory, 214
stopping times, 213
minimax quickest change detection, 228
general asymptotic minimax theory, 237
minimax algorithms, optimality properties of, 234
Shiryaev algorithm, minimax algorithms based on, 232
models, 240
variants and generalizations of the quickest change detection problem, 241
data-efficient quickest change detection, 244
distributed sensor systems, 247
with unknown pre- or post-change distributions, 241
variants of quickest change detection problem, 249
R
space-time adaptive processing, 862
astronomical phased array feeds, 885
challenges and solutions to, 891
Radio frequency interference (RFI), 876
Rao-Blackwellized particle filter, 171
Real time distributions, 116
Received signal strength (RSS), 259
Received signal strength indicator (RSSI), 804
Rectangular window function, 30
Renewal and nonlinear renewal theory, 214
RFI. See Radio frequency interference
Rihaczek distribution, 58
Rissanen’s minimum description length (MDL), 635
Road-bound vehicles, 276
Robust adaptive beamforming, 521
comparison by simulation, 544
diagonally loaded SMI beamformer, 522
doubly constrained robust adaptive beamforming, 539
eigenspace-based beamformer, 537
eigenvalue beamforming using multi-rank MVDR beamformer, 541
forward-backward averaging and spatial smoothing, 533
generalized sidelobe canceler, 527
general-rank signal model, 545
look direction mismatch (pointing error) problem, 523
LSMI adaptive beamformers, 538
motivations, 521
MVDR robust adaptive beamforming design, 536
probabilistically constrained robust adaptive beamforming, 540
rapidly moving interferences, 535
sequential quadratic programming-based robust adaptive beamforming, 540
SOI and interferences, 529
steering vector estimation, 542
wideband robust adaptive beamforming, 546
worst-case-based robust adaptive beamforming, 538
Robust Chebyshev design, 567
Robustness of algorithms, 747
robustness w.r.t. narrowband assumption, 747
Robust total least squares design, 567
Robust WLS design, 566
Role of adaptation, localization application, 340
S
Sample covariance matrix (SCM), 22
Sample matrix inversion adaptive beamformer, 514
SCM. See Sample covariance matrix (SCM)
Second-order algorithms, 743
Seismic signal analysis, 137
Semi-definite relaxation (SDR), 873
Sensor array, 819
Sensor networks, 250
Sensor networks, source localization in, 497
Sequential Monte Carlo (SMC), 167
Sequential quadratic programming-based robust adaptive beamforming, 540
Serial configuration, 195
Shiryaev algorithm, minimax algorithms based on, 232
Shiryaev-Roberts algorithm, 211
Shiryaev-Roberts-Pollak (SRP) algorithm, 232
Shiryaev-Roberts-r (SR-r) algorithm, 232
Shiryaev’s formulation, 210
Shiryaev statistic evolution, 209
Short-time Fourier transform (STFT), 28
continuous STFT inversion, 34
duration measures and uncertainty principle, 32
of multi-component signals, 35
windows, 30
Sigma points, 266
Signal eigenvectors, 610
Signal intelligence (SIGINT), 819
Signal phase derivative and distributions definitions, 112
Signal propagation models, 802
received signal strength indicator (RSSI), 804
time delay estimation, 805
Signal reconstruction, 62
Signal (source) separation problem, 802
Signal-to-noise ratio (SNR), 603
Signal to noise ratio (SNR) beamformer, 888
Simulation results, 703
R-D algorithms using matrix-based subspace estimates, 706
Simultaneous localization and mapping (SLAM), 292
Sinc distribution, 83
SINR, 823
SLAM. See Simultaneous localization and mapping (SLAM)
Small migrating animals, 290
SMC. See Sequential Monte Carlo (SMC)
S-method, 89
discrete S-method, 91
multi-component signals, decomposition of, 97
versus smoothed spectrogram, 96
Soft-thresholding function, 249
arrays, 929
matched field processing (MFP), 935
undersea acoustic channel, 932
Sound velocity, 932
Source localization algorithms, 808
non-linear least square source localization, 809
source localization using time difference of arrival, 810
Source localization and tracking
problem formulation, 800
signal propagation models, 802
source localization algorithms, 808
target tracking algorithm, 812
triangulation, 800
Source signal propagation model, 800
Sparse data representation based approach, 607
Sparse signals in time-frequency, 124
Spatial filter design, 480
Spatial filtering, 471
Spatial filtering and beam patterns, 471
Spatial time-frequency distribution (STFD), 774
SNR enhancement, 775
subspace analysis, 777
SPC. See Statistical process control (SPC)
Special array structures, 657
minimum redundancy linear arrays, 658
multidimensional arrays, 661
R-D shift invariance structure, 663
uniform rectangular arrays (URAs), 659
Specific algorithm, performance analysis of, 723
asymptotic distribution of statistics, 724
functional analysis, 723
Spherical broadband beamformer, 581
Spread sources, 493
Spread spectrum systems, interference rejection in, 139
State-space models and sequential inference, 164
Stationary phase method, 46
Statistical process control (SPC), 250
Statistical signal processing
content, 3
contributions, 4
Bayesian computational methods, 5
bounds, 6
diffusion adaptation over networks, 5
distributed signal detection, 4
geolocation, 6
model order selection, 6
non-stationary signal analysis, 5
performance analysis, 6
quickest change detection, 4
time-frequency approach, 5
historical recount, 3
Steepest-descent iterations, 351
Steerable broadband beamformer, 571
Steering vector estimation, 542
Stepwise regression, 12
STFD. See Spatial time-frequency distribution
STFT and continuous wavelet transform, 52
STFT, realizations of, 36
Stochastic complexity, concept of, 19
Stochastic matrices, 433
Stopping times, 213
algorithms using tensor-based subspace estimates, 698
multi-dimensional algorithms, 690
one-dimensional algorithms, 674
simulation results, 703
Subspace estimation, 667
matrix-based subspace estimation, 667
with small number of snapshots, 669
tensor-based subspace estimation, 672
Subspace fitting methods, 625
Subspace methods, 488
Synchronization issues, 252
algorithms for solving the imaging equation, 881
geometry and signal definitions, 878
The imaging equation, 878
T
Tapped-delay-line models, 334
Target localization, 336
Target tracking algorithm, 812
Kalman filter, 814
sequential Bayesian estimation, 813
TDoA. See Time Difference of Arrival
Tensor-based subspace estimation, 672
Time and frequency varying windows, 41
Time delay, 803
Time domain formulation, 591
Time-frequency analysis applications, 135
Time-frequency approach, 5
examples, 784
Time-frequency MUSIC, 780
Time-frequency radar signal processing, 135
Time-frequency representations
Cohen’s class of, 767
examples, 769
Time-frequency representations, affine class of, 104
Time series modeling, 495
Time-variant filtering, 138
Time varying window, 41
Total least squares design and Eigen-filters, 562
Transient change detection, 251
Transient mean-square performance, 390
Triangulation, 800
distance based triangulation, 800
generalizations, 802
geometric positions for, 801
Two-dimensional arrays, 475
U
UCA. See Uniform circular array
UKF. See Unscented Kalman filter
ULAs. See Uniform linear arrays
Uncertainty principle and Wigner distribution, 63
Undersea acoustic channel, 932
noise and reverberation, 934
propagation models, 932
Uniform data profile, 389
Uniform rectangular arrays (URAs), 659
Univariate Gaussian, 178
URAs. See Uniform rectangular arrays
V
Variants and generalizations of the quickest change detection problem, 241
Variants of quickest change detection problem, 249
Video sequence, velocities of moving objects, 138
W
Wald’s identity, 213
Watermarking, in space/spatial-frequency domain, 140
Wave equation, 579
Weighted least square (WLS) design, 561
Wideband array response, 477
Wideband DOA estimation, 631
Wideband maximum likelihood estimation, 632
Wideband robust adaptive beamforming, 546
Wigner bispectrum, 107
Wigner distribution, 60
auto-terms and cross-terms, 70
based inversion and synthesis, 76
discrete pseudo, 75
inner interferences in, 72
instantaneous bandwidth, 65
instantaneous frequency, distribution concentrated, 61
linear coordinate transforms of, 69
properties of, 67
pseudo and smoothed, 73
pseudo quantum signal representation, 64
signal reconstruction, 62
uncertainty principle and, 63
Wigner higher order spectra, 108
Wigner multi-time distribution, 110
Wireless communications, 907
multiple antennas techniques, LTE, 907
Wishart distribution, 181
Worst-case-based robust adaptive beamforming, 538
Z
Zhao-Atlas-Marks distribution, 83
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