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| Ïîèñê ïî óêàçàòåëÿì |
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| Kay S.M. — Fundamentals of statistical signal processing: estimation theory |
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| Ïðåäìåòíûé óêàçàòåëü |
ACF see "Autocorrelation"
Adaptive beamforming 544—548
Adaptive filters, Kalman 439 see sequential"
Adaptive filters, noise canceler 268—273 see sequential"
Analytic signal 497 551
ar see "Autoregressive"
ARMA see "Autoregressive moving average"
Asymptotic Cramer — Rao lower bound 51 77—81
Asymptotic efficiency 38—39 160 164
Asymptotic Gaussian PDF, complex 535
Asymptotic Gaussian PDF, real 80
Asymptotic mean and variance 295 301—302 305—306
Asymptotic MLE 190
Asymptotic probability density function of MLE 164
Asymptotic unbiasedness 38 160
Autocorrelation method of linear prediction 198
Autocorrelation, definition 575
Autocorrelation, estimator 197 204 267
Autoregressive moving average, definition 266
Autoregressive moving average, dynamic model 468
Autoregressive moving average, estimation 266—268
Autoregressive, CRLB 59—62 see
Autoregressive, definition 59—60 578 see
Autoregressive, MLE 196—198 see
Autoregressive, power spectral density, complex process 497—498 see
Autoregressive, prediction 414 see
Beamforming, conventional 547
Bearing estimation 3 57—59 195—196
Bernoulli trial 123 200
Best linear unbiased estimator, complex data 523—524
Best linear unbiased estimator, covariance errors 150
Best linear unbiased estimator, definition 134 137 139—140
Best linear unbiased estimator, derivation 151—155
Best linear unbiased estimator, linear model 141
Best linear unbiased estimator, transformations 135 147 149—150
Bias error 18
Biomedical signal processing 23
blue see "Best linear unbiased estimator"
CCF see "Cross-correlation"
Chirp rate estimator 553
Communications, channel equalization 365
Communications, coherent demodulation 273
Communications, on-off keying 148
Complete sufficient statistic 109—112 119
Complex envelope 494
Conditional mean estimator see "Minimum mean square error estimator" "Bayesian"
Consistency, estimator 24 161 200
Correlation coefficient, conditional Gaussian PDF 323
Correlation coefficient, CRLB 66
Correlation coefficient, definition 64
Correlation coefficient, least squares 241
Correlation coefficient, MLE 200 304
Correlation time 50 77—78 535
Correlator, signal 192
Cost function 342
Covariance matrix, complex, definition 501
Covariance matrix, complex, properties 505—506 555—557
Cramer — Rao lower bound, asymptotic 51 77—81
Cramer — Rao lower bound, complex Gaussian 525
Cramer — Rao lower bound, definition 22 30 39—40 44
Cramer — Rao lower bound, Gaussian PDF 47—48
Cramer — Rao lower bound, signals in WGN 36 48
Cramer — Rao lower bound, transformed parameters 37 45
CRLB see "Cramer — Rao lower bound"
Cross-correlation 514 575
Cross-power spectral density 576—577
Curve fitting, CRLB 65
Curve fitting, least squares 232—235
Curve fitting, linear model 86—88
CWGN see "White Gaussian noise complex"
Cyclical data see "Sinusoidal estimation"
DC level in noise see "Examples"
DC level in noise, definition 31
Deconvolution 365—370
Derivative, complex 499—500 517 519—521
Detection, jump in level 278
Detection, sinusoidal 98—99 148—149 554
DFT see "Discrete Fourier transform"
Digital filter design, equation error 261—265
Digital filter design, least squares 280—281
Discrete Fourier transform, normalization of 511
Discrete Fourier transform, orthogonality 89 569—570
Discrete Fourier transform, PDF for WGN 509—511 537
Dispersive channel 452
Efficiency, estimator 34 38—39 84—86 160 167 187 528
Eigenanalysis of covariance matrix 147—148 537
Eigenvalue/eigenvector 573
em see "Expectation-maximization"
entropy 336
Equation error modeling 266
Error ellipse 364
Estimators, classical vs. Bayesian 8 309 312
Estimators, combining 17
Estimators, definition 9
Estimators, performance 9—12 24 295 see mean
Estimators, selection, rationale for 489—490
Estimators, summary, Bayesian 484—485
Estimators, summary, classical 480—483
Examples, adaptive beamformer 544—548
Examples, adaptive noise canceler 268—273
Examples, autoregressive parameters in ARMA, LSE 266—268
Examples, autoregressive parameters, CRLB 59—62
Examples, autoregressive parameters, MLE 196—198
Examples, bandpass Gaussian noise 515—517
Examples, bearing, CRLB 57—59
Examples, bearing, MLE 195—196
Examples, channel estimation 452—456
Examples, covariance matrix scale factor, Bayesian estimation 329—330
Examples, curve fitting, MVU estimator 86—88
Examples, DC level and exponential in WGN, MVU estimator 96—97
Examples, DC level in colored noise, complex BLUE 523—524
Examples, DC level in colored noise, MVU estimator 95—96
Examples, DC level in noise, LSE 221
Examples, DC level in non-Gaussian noise 172—173
Examples, DC level in uncorrelated noise, BLUE 138—139
Examples, DC level in WGN, amplitude and variance sufficient statistics 118
Examples, DC level in WGN, amplitude and variance, MAP estimator 355—358
Examples, DC level in WGN, amplitude/variance, MLE 158—163
Examples, DC level in WGN, biased estimator 17
Examples, DC level in WGN, CRLB for amplitude 31—32
Examples, DC level in WGN, CRLB for amplitude and variance 40—41
Examples, DC level in WGN, CRLB for random amplitude variance 49—50
Examples, DC level in WGN, Gaussian prior, MMSE estimator 317—321 326—328 360—361
Examples, DC level in WGN, method of moments 291—292
Examples, DC level in WGN, MLE for amplitude 163—164
Examples, DC level in WGN, MLE for amplitude and variance 183
Examples, DC level in WGN, MLE Monte Carlo performance 164—166
Examples, DC level in WGN, MVU amplitude and variance estimator from sufficient statistic 119—122
Examples, DC level in WGN, MVU amplitude estimator from sufficient statistic 107—109
Examples, DC level in WGN, sequential LMMSE estimator 392—393
Examples, DC level in WGN, sequential LSE 243—248
Examples, DC level in WGN, sufficient statistic 105
Examples, DC level in WGN, transformed parameter MLE 173—177
Examples, DC level in WGN, unbiased estimator 16
Examples, DC level in WGN, uniform prior, LMMSE estimator 383
Examples, DC level in WGN, uniform prior, MAP estimator 352—353
Examples, DC level in WGN, uniform prior, MMSE estimator 315
Examples, DC level in white noise, BLUE 137—138
Examples, digital filter design, LSE 261—265
Examples, discrete Fourier transform, PDF of CWGN 535—537
Examples, discrete Fourier transform, PDF of WGN 509—511
Examples, exponential PDF parameter transformation, MAP estimator 358—359
Examples, exponential PDF parameter, MAP estimator 351—352
Examples, exponential PDF parameter, method of moments 292 295—297
Examples, exponential signal in WGN, MLE 178—182
Examples, exponential signal in white noise, ad-hoc estimator 298—299
Examples, exponential signal, LSE 257—258
Examples, Fourier analysis, Bayesian 347—349 362—364 399—400
Examples, Fourier analysis, LSE 226—227 230—231
Examples, Fourier analysis, MVU estimator 88—90
| Examples, Fourier analysis, sequential LSE 250—251
Examples, frequencies of sinusoids, EM estimator 187—189
Examples, frequency of sinusoid, CRLB 36
Examples, frequency of sinusoid, method of moments 299—304
Examples, frequency of WSS process, center, CRLB 51—53
Examples, Gauss — Markov model 427—428
Examples, Gaussian mixture parameters 290—291 293—294
Examples, Hermitian form, mean and variance 512—513
Examples, Hermitian function, minimization 521—523
Examples, identification of FIR system, MVU estimator 90—94
Examples, Kalman filter 436—438 443—445
Examples, line fitting, CRLB 41—43
Examples, line fitting, order-recursive LSE 237—240
Examples, linear model, classical complex 529—530
Examples, localization, source, BLUE 142—146
Examples, mean of uniform noise, MVU estimator 113—116
Examples, moving average, MLE 190—191
Examples, MVU estimator, possible nonexistence of 20—21
Examples, orthogonal random variables, LMMSE estimator 388—389
Examples, PDF parameter dependence 28—31
Examples, periodogram spectral estimation 538—539
Examples, phase of complex sinusoid, MLE 531—532
Examples, phase of sinusoid, CRLB 33—34
Examples, phase of sinusoid, MLE 167—172
Examples, phase of sinusoid, sufficient statistic 106—107
Examples, phase-locked loop 273—275
Examples, power of noise, CRLB 49
Examples, power of noise, sufficient statistic 105
Examples, range, CRLB 53—56
Examples, range, MLE 192
Examples, signal amplitude estimation, complex LSE 498—500
Examples, signal in non-Gaussian noise, MLE 184—185
Examples, signal in WGN, CRLB 48
Examples, signal, constrained LSE 252—254
Examples, signal-to-noise ratio, CRLB 46
Examples, sinusoidal amplitude, LSE 255—256
Examples, sinusoidal complex amplitude, MMSE estimator 534—535
Examples, sinusoidal modeling, complex 496—497
Examples, sinusoidal parameters, complex MLE 539—544
Examples, sinusoidal parameters, CRLB 56—57
Examples, sinusoidal parameters, LSE 222—223
Examples, sinusoidal parameters, MLE 193—195
Examples, sinusoidal parameters, sufficient statistics 117—118
Examples, sinusoidal power, complex MVU estimator 525—527
Examples, sufficient statistic verification 103—104
Examples, sufficient statistic, completeness of 110—111
Examples, sufficient statistic, incompleteness of 111—112
Examples, vehicle tracking 456—466
Examples, Wiener filtering 365—370 400—409 443—445
Expectation-Maximization 182 187—189
Exponential PDF family, definition see "Probability density functions"
Exponential PDF family, MLE 200
Exponential signals, estimation 257—258 298—299
Fading signal 100 452
Finite impulse response filter 90—94
FIR see "Finite impulse response filter"
Fisher information, decoupled matrix 41 65
Fisher information, definition 34 40
Fisher information, properties 35 65
Fourier analysis 88—90 226—227 250—251 347—349 362—364 399—400
Frequency estimation see "Sinusoidal estimation and Examples"
Gauss — Markov process, definition 421 426 430—431
Gauss — Markov process, properties 424 429
Gauss — Markov theorem 141 143 552
Gauss — Newton iteration 260
Gaussian random process 467 513 577—578
Gradient formulas 73—74 84 519—521
Gram — Schmidt orthogonalization 236 396 411
Grid search 177
Hermitian form, definition 502
Hermitian form, minimization 521—523
Hermitian form, moments 502—503 513
histogram 10 165 206—207 209
Image signal processing 365
In-phase signal 495—496
Innovations 396 433 441
interference suppression 270
Interpolation 412
Kalman filter, definition 436 446—449 455
Kalman filter, derivation 471—475
Kalman filter, extended 451—452 462 476—477
Kalman filter, gain 436 447
Kalman filter, information form 449
Kalman filter, steady state 443
Least squares, BLUE, relationship with 225
Least squares, constrained 252
Least squares, definition 220—221
Least squares, estimator 225
Least squares, modified Yule — Walker equations 268
Least squares, nonlinear 222 254
Least squares, numerical determination 259—260
Least squares, order-recursive 237 282—284
Least squares, separable 222—223 256—257
Least squares, sequential 249 279 286—288
Least squares, weighted 150 225—226 244—248 270
Levinson recursion 198 403
Likelihood function, definition 29
Likelihood function, modified 175 185
Line arrays 58 145
Line fitting 41 83—84 237—240 373
Linear minimum mean square error estimator, definition 380—382 389
Linear minimum mean square error estimator, properties 390
Linear minimum mean square error estimator, sequential 393 398 415—418
Linear minimum mean square error estimator, vector space interpretation 386
Linear model (Bayesian), definition 325
Linear model (Bayesian), Kalman filter modeling 447
Linear model (Bayesian), MMSE estimator 364—365 533—534
Linear model (Bayesian), properties 487—489
Linear model (classical), CRLB 85
Linear model (classical), definition 84 94—95 97 529—530
Linear model (classical), efficiency 85—86
Linear model (classical), estimator and properties 85 486—488
Linear model (classical), line fitting 45
Linear model (classical), MLE 186
Linear model (classical), reduced 99 254
Linear model (classical), sufficient statistics 126
Linear Predictive Coding 5 59 198 407
Linear random process 77
LMMSE see "Linear minimum mean square error estimator"
Localization, source 142—146 456—466
LPC see "Linear predictive coding"
LS, LSE see "Least squares"
Lyapunov equation 430
MA see "Moving average"
MAP see "Maximum a posteriori estimator"
Matrix, autocorrelation 62 93
Matrix, determinant 567
Matrix, diagonal 568—569
Matrix, eigenanalysis 573
Matrix, hermitian 501
Matrix, idem potent 194 570
Matrix, ill-conditioned 85 98 240—241
Matrix, inversion, definition 567
Matrix, inversion, lemma 571
Matrix, inversion, Woodbury's identity 571
Matrix, orthogonal 569
Matrix, partitioned 571—572
Matrix, positive definite (semidefinite) 568 572
Matrix, projection 231 242 277 285
Matrix, square 567
Matrix, symmetric 567
Matrix, Toeplitz 62 93 570
Matrix, trace 568
Matrix, transpose 567
Maximum a posteriori estimator, definition 344 351 354 372
Maximum a posteriori estimator, properties 358 372
Maximum likelihood estimator, asymptotic 190
Maximum likelihood estimator, Bayesian 352
Maximum likelihood estimator, complex data 530—531 563—565
Maximum likelihood estimator, definition 162 182
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