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Kay S.M. — Fundamentals of statistical signal processing, volume 1: estimation theory
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Íàçâàíèå: Fundamentals of statistical signal processing, volume 1: estimation theoryÀâòîð: Kay S.M. Àííîòàöèÿ: This text is geared towards a one-semester graduate-level course in statistical signal processing and estimation theory. The author balances technical detail with practical and implementation issues, delivering an exposition that is both theoretically rigorous and application-oriented. The book covers topics such as minimum variance unbiased estimators, the Cramer-Rao bound, best linear unbiased estimators, maximum likelihood estimation, recursive least squares, Bayesian estimation techniques, and the Wiener and Kalman filters. The author provides numerous examples, which illustrate both theory and applications for problems such as high-resolution spectral analysis, system identification, digital filter design, adaptive beamforming and noise cancellation, and tracking and localization. The primary audience will be those involved in the design and implementation of optimal estimation algorithms on digital computers. The text assumes that you have a background in probability and random processes and linear and matrix algebra and exposure to basic signal processing. Students as well as researchers and practicing engineers will find the text an invaluable introduction and resource for scalar and vector parameter estimation theory and a convenient reference for the design of successive parameter estimation algorithms.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Âåðîÿòíîñòü /Ñòàòèñòèêà è ïðèëîæåíèÿ /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1993Êîëè÷åñòâî ñòðàíèö: 595Äîáàâëåíà â êàòàëîã: 04.06.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
ACF (see Autocorrelation) Adaptive beamforming 544—48 Adaptive filters (see Least squares sequential) Adaptive filters, Analytic signal 497 551 Adaptive filters, Kalman 439 Adaptive filters, noise canceler 268—73 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—2 305-6 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 (see also Linear predictive coding) Autoregressive moving average, definition 266 Autoregressive moving average, dynamic model 468 Autoregressive moving average, estimation 266—68 Autoregressive, definition 59—60 578 Autoregressive, MLE 196—98 Autoregressive, ORLB 59—62 Autoregressive, power spectral density, complex process 497—98 Autoregressive, prediction 414 Bayesian 484—85 Beamforming, conventional 547 Bearing estimation 3 57—59 195—96 Bernoulli trial 123 200 Best linear unbiased estimator, complex data 523—24 Best linear unbiased estimator, covariance errors 150 Best linear unbiased estimator, definition 134 137 139—40 Best linear unbiased estimator, derivation 151—55 Best linear unbiased estimator, linear model 141 Best linear unbiased estimator, transformations 135 147 149—50 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—12 119 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—6 555—57 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—77 Curve fitting, CRLB 65 Curve fitting, least squares 232—35 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, Deconvolution 365—70 DC level in noise, definition 31 Derivative, complex 499—500 517 519—21 Detection, jump in level 278 Detection, sinusoidal 98—99 148—49 554 DFT (see Discrete Fourier transform) Digital filter design, equation error 261—65 Digital filter design, least squares 280—81 Discrete Fourier transform, normalization of 511 Discrete Fourier transform, orthogonality 89 569—70 Discrete Fourier transform, PDF for WGN 509—11 537 Dispersive channel 452 Efficiency, estimator 34 38—39 84—86 160 167 187 528 Eigenanalysis of covariance matrix 147—48 537 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 mean Estimators, selection, rationale for 489—90 Estimators, summary, classical 480—83 Examples, adaptive beamformer 544—48 5 Examples, adaptive noise canceler 268—73 Examples, autoregressive parameters in ARMA, LSE 266—68 Examples, autoregressive parameters, CRLB 59—62 Examples, autoregressive parameters, MLE 196—98 Examples, bandpass Gaussian noise 515—17 Examples, bearing, CRLB 57—59 Examples, bearing, MLE 195—96 Examples, channel estimation 452—56 Examples, covariance matrix scale factor, Bayesian estimation 329—30 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—24 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—73 Examples, DC level in uncorrelated noise, BLUE 138—39 Examples, DC level in WGN, amplitude and variance sufficient statistics 118 Examples, DC level in WGN, amplitude and variance, MAP estimator 355—58 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—21 326—28 360-61 Examples, DC level in WGN, method of moments 291—92 Examples, DC level in WGN, MLE for amplitude and variance 183 Examples, DC level in WGN, MLE Monte Carlo performance 164—66 Examples, DC level in WGN, MVU amplitude and variance estimator from sufficient statistic 119—22 Examples, DC level in WGN, MVU amplitude estimator from sufficient statistic 107—109 Examples, DC level in WGN, sequential LMMSE estimator 392—93 Examples, DC level in WGN, sequential LSE 243—48 Examples, DC level in WGN, sufficient statistic 105 Examples, DC level in WGN, transformed parameter MLE 173—77 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—53 Examples, DC level in WGN. MLE for amplitude 163—64 Examples, DC level in WGN. uniform prior, MMSE estimator 315 Examples, DC level in white noise, BLUE 137—38 Examples, digital filter design, LSE 261—65 Examples, discrete Fourier transform, PDF of CWGN 535—37 Examples, discrete Fourier transform, PDF of WGN 509—11 Examples, estimator 298—99 Examples, exponential PDF parameter transformation, MAP estimator 358—59 Examples, exponential PDF parameter, MAP estimator 351—52 Examples, exponential PDF parameter, method of moments 292 295—97 Examples, exponential signal in WGN, MLE 178—82 Examples, exponential signal, LSE 257—58 Examples, Fourier analysis, Bayesian 347—49 362—64 399—400 Examples, Fourier analysis, LSE 226—27 230—31 Examples, Fourier analysis, MVU estimator 88—90 Examples, Fourier analysis, sequential LSE 250—51 Examples, frequencies of sinusoids, EM estimator 187—89 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—28 Examples, Gaussian mixture parameters 290—91 293—94 Examples, Hermitian form, mean and variance 512—13 Examples, Hermitian function, minimization 521—23 Examples, identification of FIR system, MVU estimator 90—94 Examples, Kalman filter 436—38 443—45 Examples, line fitting, CRLB 41—43 Examples, line fitting, order-recursive LSE 237—40 Examples, linear model, classical complex 529—30 Examples, localization, source, BLUE 142—46 Examples, mean of uniform noise, MVU estimator 113—16 Examples, moving average, MLE 190—91 Examples, MVU estimator, possible nonexistence of 20—21 Examples, orthogonal random variables. LMMSE estimator 388—89 Examples, PDF parameter dependence 28—31 Examples, periodogram spectral estimation 538—39 Examples, phase of complex sinusoid, MLE 531—32 Examples, phase of sinusoid, CRLB 33—34 Examples, phase of sinusoid, MLE 167—72 Examples, phase of sinusoid, sufficient statistic 106—7 Examples, phase-locked loop 273—75 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—85 Examples, signal in WGN, CRLB 48 Examples, signal, constrained LSE 252—54 Examples, signal-to-noise ratio. CRLB 46 Examples, sinusoidal amplitude, LSE 255—56 Examples, sinusoidal complex amplitude, MMSE estimator 534—35 Examples, sinusoidal modeling, complex 496—97 Examples, sinusoidal parameters, complex MLE 539—44 Examples, sinusoidal parameters, CRLB 56—57 Examples, sinusoidal parameters, LSE 222—23 Examples, sinusoidal parameters, MLE 193—95 Examples, sinusoidal parameters, sufficient statistics 117—18 Examples, sinusoidal power, complex MVU estimator 525—27 Examples, sufficient statistic verification 103—4 Examples, sufficient statistic, completeness of 110—11 Examples, sufficient statistic, incompleteness of 111—12 Examples, vehicle tracking 456—66 Examples, Wiener filtering 365—70 400—409 443-45 Expectation-Maximization 182 187—89 Exponential PDF family, definition (see Probability density functions) Exponential PDF family, MLE 200 Exponential signals, estimation 257 58 298—99 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—27 250-51 347—49 362—64 399-400 Frequency estimation (see Sinusoidal estimation and Examples) Gauss — Markov theorem 141 143 552 Gauss — Newton iteration 260 Gauss-Markov process, definition 421 426 430—31 Gauss-Markov process, properties 424 429 Gaussian random process 467 513 577—78 Gradient formulas 73—74 84 519—21 Gram — Schmidt orthogonalization 236 396 411 Grid search 177 Hermitian form, definition 502 Hermitian form, minimization 521—23 Hermitian form, moments 502—3 513 histogram 10 165 206—7 209 Image signal processing 365 In-phase signal 495—96 Innovations 396 433 441 interference suppression 270 Interpolation 412 Kalman filter, definition 436 446—49 455 Kalman filter, derivation 471—75 Kalman filter, extended 451—52 462 476—77 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—21 Least squares, estimator 225 Least squares, modified Yule — Walker equations 268 Least squares, nonlinear 222 254 Least squares, numerical determination 259—60 Least squares, order-recursive 237 282—84 Least squares, separable 222—23 256—57 Least squares, sequential 249 279 286—88 Least squares, weighted 150 225—26 244—48 270 Levinson recursion 198 403 Likelihood function, definition 29 Likelihood function, modified 175 185 Line arrays 58 145 Line fitting 41 83—84 237—40 373 Linear minimum mean square error estimator, definition 380—82 389 Linear minimum mean square error estimator, properties 390 Linear minimum mean square error estimator, sequential 393 398 415—18 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—65 533—34 Linear model (Bayesian), properties 487—89 Linear model (classical), CRLB 85 Linear model (classical), definition 84 94—95 97 529—30 Linear model (classical), efficiency 85—86 Linear model (classical), estimator and properties 85 486—88 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—46 456—66 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—69 Matrix, eigenanalysis 573 Matrix, hermitian 501 Matrix, idempotent 194 570 Matrix, ill-conditioned 85 98 240—41 Matrix, inversion, definition 567 Matrix, inversion, lemma 571 Matrix, inversion, orthogonal 569 Matrix, inversion, partitioned 571—72 Matrix, inversion, positive definite (semidefinite) 568 572 Matrix, inversion, projection 231 242 277 285 Matrix, inversion, square 567 Matrix, inversion, symmetric 567 Matrix, inversion, Toeplitz 62 93 570 Matrix, inversion, trace 568 Matrix, inversion, transpose 567 Matrix, inversion, Woodbury's identity 571 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
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