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Kay S.M. Ч Fundamentals of statistical signal processing, volume 1: estimation theory
Kay S.M. Ч Fundamentals of statistical signal processing, volume 1: estimation theory

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Ќазвание: Fundamentals of statistical signal processing, volume 1: estimation theory

јвтор: Kay S.M.


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.

язык: en

–убрика: ћатематика/¬еро€тность/—татистика и приложени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1993

 оличество страниц: 595

ƒобавлена в каталог: 04.06.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
ACF      (see Autocorrelation)
Adaptive beamforming      544Ч48
Adaptive filters      (see Least squares sequential)
Adaptive filters, Analytic signal      497 551
Adaptive filters, Kalman      439
Adaptive filters, noise canceler      268Ч73
ar      (see Autoregressive)
ARMA      (see Autoregressive moving average)
Asymptotic, Cramer Ч Rao lower bound      51 77Ч81
Asymptotic, efficiency      38Ч39 160 164
Asymptotic, Gaussian PDF, complex      535
Asymptotic, Gaussian PDF, real      80
Asymptotic, mean and variance      295 301Ч2 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      266Ч68
Autoregressive, definition      59Ч60 578
Autoregressive, MLE      196Ч98
Autoregressive, ORLB      59Ч62
Autoregressive, power spectral density, complex process      497Ч98
Autoregressive, prediction      414
Bayesian      484Ч85
Beamforming, conventional      547
Bearing estimation      3 57Ч59 195Ч96
Bernoulli trial      123 200
Best linear unbiased estimator, complex data      523Ч24
Best linear unbiased estimator, covariance errors      150
Best linear unbiased estimator, definition      134 137 139Ч40
Best linear unbiased estimator, derivation      151Ч55
Best linear unbiased estimator, linear model      141
Best linear unbiased estimator, transformations      135 147 149Ч50
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      109Ч12 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 77Ч78 535
Correlator, signal      192
Cost function      342
Covariance matrix, complex, definition      501
Covariance matrix, complex, properties      505Ч6 555Ч57
Cramer-Rao lower bound, asymptotic      51 77Ч81
Cramer-Rao lower bound, complex Gaussian      525
Cramer-Rao lower bound, definition      22 30 39Ч40 44
Cramer-Rao lower bound, Gaussian PDF      47Ч48
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      576Ч77
Curve fitting, CRLB      65
Curve fitting, least squares      232Ч35
Curve fitting, linear model      86Ч88
CWGN      (see White Gaussian noise complex)
Cyclical data      (see Sinusoidal estimation)
DC level in noise      (see Examples)
DC level in noise, Deconvolution      365Ч70
DC level in noise, definition      31
Derivative, complex      499Ч500 517 519Ч21
Detection, jump in level      278
Detection, sinusoidal      98Ч99 148Ч49 554
DFT      (see Discrete Fourier transform)
Digital filter design, equation error      261Ч65
Digital filter design, least squares      280Ч81
Discrete Fourier transform, normalization of      511
Discrete Fourier transform, orthogonality      89 569Ч70
Discrete Fourier transform, PDF for WGN      509Ч11 537
Dispersive channel      452
Efficiency, estimator      34 38Ч39 84Ч86 160 167 187 528
Eigenanalysis of covariance matrix      147Ч48 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      9Ч12 24 295 mean
Estimators, selection, rationale for      489Ч90
Estimators, summary, classical      480Ч83
Examples, adaptive beamformer      544Ч48 5
Examples, adaptive noise canceler      268Ч73
Examples, autoregressive parameters in ARMA, LSE      266Ч68
Examples, autoregressive parameters, CRLB      59Ч62
Examples, autoregressive parameters, MLE      196Ч98
Examples, bandpass Gaussian noise      515Ч17
Examples, bearing, CRLB      57Ч59
Examples, bearing, MLE      195Ч96
Examples, channel estimation      452Ч56
Examples, covariance matrix scale factor, Bayesian estimation      329Ч30
Examples, curve fitting, MVU estimator      86Ч88
Examples, DC level and exponential in WGN, MVU estimator      96Ч97
Examples, DC level in colored noise, complex BLUE      523Ч24
Examples, DC level in colored noise, MVU estimator      95Ч96
Examples, DC level in noise, LSE      221
Examples, DC level in non Ч Gaussian noise      172Ч73
Examples, DC level in uncorrelated noise, BLUE      138Ч39
Examples, DC level in WGN, amplitude and variance sufficient statistics      118
Examples, DC level in WGN, amplitude and variance, MAP estimator      355Ч58
Examples, DC level in WGN, amplitude/variance, MLE      158Ч163
Examples, DC level in WGN, biased estimator      17
Examples, DC level in WGN, CRLB for amplitude      31Ч32
Examples, DC level in WGN, CRLB for amplitude and variance      40Ч41
Examples, DC level in WGN, CRLB for random amplitude variance      49Ч50
Examples, DC level in WGN, Gaussian prior, MMSE estimator      317Ч21 326Ч28 360-61
Examples, DC level in WGN, method of moments      291Ч92
Examples, DC level in WGN, MLE for amplitude and variance      183
Examples, DC level in WGN, MLE Monte Carlo performance      164Ч66
Examples, DC level in WGN, MVU amplitude and variance estimator from sufficient statistic      119Ч22
Examples, DC level in WGN, MVU amplitude estimator from sufficient statistic      107Ч109
Examples, DC level in WGN, sequential LMMSE estimator      392Ч93
Examples, DC level in WGN, sequential LSE      243Ч48
Examples, DC level in WGN, sufficient statistic      105
Examples, DC level in WGN, transformed parameter MLE      173Ч77
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      352Ч53
Examples, DC level in WGN. MLE for amplitude      163Ч64
Examples, DC level in WGN. uniform prior, MMSE estimator      315
Examples, DC level in white noise, BLUE      137Ч38
Examples, digital filter design, LSE      261Ч65
Examples, discrete Fourier transform, PDF of CWGN      535Ч37
Examples, discrete Fourier transform, PDF of WGN      509Ч11
Examples, estimator      298Ч99
Examples, exponential PDF parameter transformation, MAP estimator      358Ч59
Examples, exponential PDF parameter, MAP estimator      351Ч52
Examples, exponential PDF parameter, method of moments      292 295Ч97
Examples, exponential signal in WGN, MLE      178Ч82
Examples, exponential signal, LSE      257Ч58
Examples, Fourier analysis, Bayesian      347Ч49 362Ч64 399Ч400
Examples, Fourier analysis, LSE      226Ч27 230Ч31
Examples, Fourier analysis, MVU estimator      88Ч90
Examples, Fourier analysis, sequential LSE      250Ч51
Examples, frequencies of sinusoids, EM estimator      187Ч89
Examples, frequency of sinusoid, CRLB.      36
Examples, frequency of sinusoid, method of moments      299Ч304
Examples, frequency of WSS process, center, CRLB      51Ч53
Examples, Gauss Ч Markov model      427Ч28
Examples, Gaussian mixture parameters      290Ч91 293Ч94
Examples, Hermitian form, mean and variance      512Ч13
Examples, Hermitian function, minimization      521Ч23
Examples, identification of FIR system, MVU estimator      90Ч94
Examples, Kalman filter      436Ч38 443Ч45
Examples, line fitting, CRLB      41Ч43
Examples, line fitting, order-recursive LSE      237Ч40
Examples, linear model, classical complex      529Ч30
Examples, localization, source, BLUE      142Ч46
Examples, mean of uniform noise, MVU estimator      113Ч16
Examples, moving average, MLE      190Ч91
Examples, MVU estimator, possible nonexistence of      20Ч21
Examples, orthogonal random variables. LMMSE estimator      388Ч89
Examples, PDF parameter dependence      28Ч31
Examples, periodogram spectral estimation      538Ч39
Examples, phase of complex sinusoid, MLE      531Ч32
Examples, phase of sinusoid, CRLB      33Ч34
Examples, phase of sinusoid, MLE      167Ч72
Examples, phase of sinusoid, sufficient statistic      106Ч7
Examples, phase-locked loop      273Ч75
Examples, power of noise, CRLB      49
Examples, power of noise, sufficient statistic      105
Examples, range, CRLB      53Ч56
Examples, range, MLE      192
Examples, signal amplitude estimation, complex LSE      498Ч500
Examples, signal in non Ч Gaussian noise, MLE      184Ч85
Examples, signal in WGN, CRLB      48
Examples, signal, constrained LSE      252Ч54
Examples, signal-to-noise ratio. CRLB      46
Examples, sinusoidal amplitude, LSE      255Ч56
Examples, sinusoidal complex amplitude, MMSE estimator      534Ч35
Examples, sinusoidal modeling, complex      496Ч97
Examples, sinusoidal parameters, complex MLE      539Ч44
Examples, sinusoidal parameters, CRLB      56Ч57
Examples, sinusoidal parameters, LSE      222Ч23
Examples, sinusoidal parameters, MLE      193Ч95
Examples, sinusoidal parameters, sufficient statistics      117Ч18
Examples, sinusoidal power, complex MVU estimator      525Ч27
Examples, sufficient statistic verification      103Ч4
Examples, sufficient statistic, completeness of      110Ч11
Examples, sufficient statistic, incompleteness of      111Ч12
Examples, vehicle tracking      456Ч66
Examples, Wiener filtering      365Ч70 400Ч409 443-45
Expectation-Maximization      182 187Ч89
Exponential PDF family, definition      (see Probability density functions)
Exponential PDF family, MLE      200
Exponential signals, estimation      257 58 298Ч99
Fading signal      100 452
Finite impulse response filter      90Ч94
FIR      (see Finite impulse response filter)
Fisher information, decoupled matrix      41 65
Fisher information, definition      34 40
Fisher information, properties      35 65
Fourier analysis      88Ч90 226Ч27 250-51 347Ч49 362Ч64 399-400
Frequency estimation      (see Sinusoidal estimation and Examples)
Gauss Ч Markov theorem      141 143 552
Gauss Ч Newton iteration      260
Gauss-Markov process, definition      421 426 430Ч31
Gauss-Markov process, properties      424 429
Gaussian random process      467 513 577Ч78
Gradient formulas      73Ч74 84 519Ч21
Gram Ч Schmidt orthogonalization      236 396 411
Grid search      177
Hermitian form, definition      502
Hermitian form, minimization      521Ч23
Hermitian form, moments      502Ч3 513
histogram      10 165 206Ч7 209
Image signal processing      365
In-phase signal      495Ч96
Innovations      396 433 441
interference suppression      270
Interpolation      412
Kalman filter, definition      436 446Ч49 455
Kalman filter, derivation      471Ч75
Kalman filter, extended      451Ч52 462 476Ч77
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      220Ч21
Least squares, estimator      225
Least squares, modified Yule Ч Walker equations      268
Least squares, nonlinear      222 254
Least squares, numerical determination      259Ч60
Least squares, order-recursive      237 282Ч84
Least squares, separable      222Ч23 256Ч57
Least squares, sequential      249 279 286Ч88
Least squares, weighted      150 225Ч26 244Ч48 270
Levinson recursion      198 403
Likelihood function, definition      29
Likelihood function, modified      175 185
Line arrays      58 145
Line fitting      41 83Ч84 237Ч40 373
Linear minimum mean square error estimator, definition      380Ч82 389
Linear minimum mean square error estimator, properties      390
Linear minimum mean square error estimator, sequential      393 398 415Ч18
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      364Ч65 533Ч34
Linear model (Bayesian), properties      487Ч89
Linear model (classical), CRLB      85
Linear model (classical), definition      84 94Ч95 97 529Ч30
Linear model (classical), efficiency      85Ч86
Linear model (classical), estimator and properties      85 486Ч88
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      142Ч46 456Ч66
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      568Ч69
Matrix, eigenanalysis      573
Matrix, hermitian      501
Matrix, idempotent      194 570
Matrix, ill-conditioned      85 98 240Ч41
Matrix, inversion, definition      567
Matrix, inversion, lemma      571
Matrix, inversion, orthogonal      569
Matrix, inversion, partitioned      571Ч72
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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