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| Kay S.M. — Fundamentals of statistical signal processing: estimation theory |
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| Предметный указатель |
Maximum likelihood estimator, efficiency 164 187
Maximum likelihood estimator, Gaussian PDF 185
Maximum likelihood estimator, invariance 174—176 185
Maximum likelihood estimator, numerical determination 177—182 187—189
Maximum likelihood estimator, probability density function, asymptotic 167 183 211—213
Maximum likelihood estimator, properties, asymptotic 172 201—202
Mean square bandwidth 55
Mean square error matrix 361—362 390
Mean square error, Bayesian 311 320 347 533
Mean square error, classical 19
Minimal sufficient statistic 102 117
Minimum mean square error estimator, Bayesian definition 313 316 346
Minimum mean square error estimator, Bayesian performance 360 364—365 534
Minimum mean square error estimator, Bayesian properties 349—350
Minimum mean square error estimator, classical 19 311
Minimum variance distortionless response 546
Minimum variance unbiased estimator, definition 20
Minimum variance unbiased estimator, determination of 109 112—113
Minimum variance unbiased estimator, linear model 85—86
MLE see "Maximum likelihood estimator"
MMSE see "Minimum mean square error estimator"
Modeling, dynamical signal 421
Modeling, identifiability 85
Modeling, least squares 232—234
Modeling, linearization 143 259 273 451 461
Modeling, speech spectrum 5 see
Moments, method of definition 293
Moments, method of exponential parameter, estimator 292 295—297
Moments, method of Gaussian mixture 290—291 293—294
Monte Carlo method 10 164—167 205—210
Moving average, asymptotic MLE 190—191
Moving average, definition 580
MSE see "Mean square error"
MVU see "Minimum variance unbiased estimator"
Narrowband representation 495
Newton — Raphson iteration 179—182 187 259
Neyman — Fisher factorization 104—105 117 127—129
Normal equations 225 387
Notational conventions 13
Nuisance parameters 329
Observation equation 446
Observation matrix 84 100 140 224
Order statistics 114
Orthogonality 89 385 see orthogonal"
Outliers 170
PDF see "Probability density functions"
Periodogram 80 190 195 197 204 see
Phase-locked loop 273—275
Posterior PDF, Bayesian linear model 326 533
Posterior PDF, definition 313 317
Power estimation, random process 66 203 553—554
Power spectral density 576—577
Prediction, Kalman 440—441 469—470
Prediction, Wiener 400
Prior PDF, conjugate 335 see
Prior PDF, definition 313
Prior PDF, noninformative 332 336
Probability density functions, chi—squared 122 575
Probability density functions, complex Gaussian, conditional 508—509 562
Probability density functions, complex Gaussian, definition 503—504 507
Probability density functions, complex Gaussian, properties 508—509 550 558—562
Probability density functions, exponential 122
Probability density functions, exponential family 110 124
Probability density functions, gamma, inverted 329—330 355
Probability density functions, Gaussian 574
Probability density functions, Gaussian mixture 150
Probability density functions, Gaussian, conditional 323—325 337—339
Probability density functions, Laplacian 63
Probability density functions, lognormal 147
Probability density functions, Rayleigh 122 371
Processing gain 554
Projection theorem, orthogonal 228—229 386
Prony method 264
| PSD see "Power spectral density"
Pseudorandom noise 92 165 206
Pythagorean theorem, least squares 276
Quadratic form, definition 568
Quadratic form, moments 76
Quadrature signal 495—496
Radar signal processing 1
Random number generator see "Pseudorandom noise"
Random variable, complex 500—501
Range estimation 1 14 53—56 192
Rao — Blackwell — Lehmann — Scheffe theorem 22 109 118—119 130—131
Rayleigh fading 347
RBLs see "Rao — Blackwell — Lehmann — Scheffe theorem"
Regression, nonlinear 254
Regularity conditions 30 44 63 67 70
Reproducing PDF 321 334—335
Ricatti equation 443
Risk, Bayes 342
Sample mean estimator 115 121 164 see
Sample variance estimator 121 164
Scoring 180 187
Seismic signal processing 365
Separability, least squares 222—223 256
Signal amplitude estimator 136 498—500
Sinusoidal estimation, amplitudes 88—90
Sinusoidal estimation, complex data 525—527 531—532 534—535 543
Sinusoidal estimation, CRLB for frequency 36
Sinusoidal estimation, CRLB for parameters 56—57 542
Sinusoidal estimation, CRLB for phase 33
Sinusoidal estimation, EM for frequency 187—189
Sinusoidal estimation, least squares for parameters 255—256
Sinusoidal estimation, method of moments for frequency 300 306
Sinusoidal estimation, MLE for parameters 193—195 203—204
Sinusoidal estimation, phase estimator 123 167—172
Sinusoidal estimation, sufficient statistics 117—118
Sinusoidal modeling, complex 496
Slutsky's theorem 201
Smoothing, Wiener 400
Sonar signal processing 2
Spatial frequency 58 195
Spectral estimation, autoregressive 60
Spectral estimation, Fourier analysis 88—90
Spectral estimation, periodogram 204 538—539 543 552
Speech recognition 4
State transition matrix 426
State vector 424
Statistical linearization 39 200 see
Sufficient statistic 22 102—103 107 116
System identification, nonrandom FIR 90—94 99
System identification, random FIR 452—455
Tapped delay line see "FIR"
Threshold effect 170
Time delay estimation 53—56 142—146
Time difference of arrival 142
Time series 6
Tracking, frequency 470 see
Tracking, frequency vehicle position 456—466
Unbiased estimator 16 22
Vector spaces, least squares 227—230
Vector spaces, random variables 384
Wavenumber see "Spatial frequency"
WGN see "White Gaussian noise"
White Gaussian noise, complex 517
White Gaussian noise, real 7
White noise 576
Whitening, Kalman 441 444
Whitening, matrix transformation 94—96
Wide sense stationary 575
Wiener filtering 365—370 373—374 379 400—409 443
Wiener — Hopf equations, filtering 403
Wiener — Hopf equations, prediction 406—407
WSS see "Wide sense stationary"
Yule — Walker equations, AR 198 579
Yule — Walker equations, ARMA 267
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