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Haykin S. — Kalman filtering and neural networks
Haykin S. — Kalman filtering and neural networks

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Название: Kalman filtering and neural networks

Автор: Haykin S.

Аннотация:

State-of-the-art coverage of Kalman filter methods for the design of neural networks
This self-contained book consists of seven chapters by expert contributors that discuss Kalman filtering as applied to the training and use of neural networks. Although the traditional approach to the subject is almost always linear, this book recognizes and deals with the fact that real problems are most often nonlinear.
The first chapter offers an introductory treatment of Kalman filters with an emphasis on basic Kalman filter theory, Rauch-Tung-Striebel smoother, and the extended Kalman filter. Other chapters cover:
* An algorithm for the training of feedforward and recurrent multilayered perceptrons, based on the decoupled extended Kalman filter (DEKF)
* Applications of the DEKF learning algorithm to the study of image sequences and the dynamic reconstruction of chaotic processes
* The dual estimation problem
* Stochastic nonlinear dynamics: the expectation-maximization (EM) algorithm and the extended Kalman smoothing (EKS) algorithm
* The unscented Kalman filter
Each chapter, with the exception of the introduction, includes illustrative applications of the learning algorithms described here, some of which involve the use of simulated and real-life data. Kalman Filtering and Neural Networks serves as an expert resource for researchers in neural networks and nonlinear dynamical systems.


Язык: en

Рубрика: Computer science/Генетика, нейронные сети/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 284

Добавлена в каталог: 17.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"Joseph" version of the covariance update equation      8
"What" pathway      79
"Where" pathway      80
A priori covariance matrix      7
Air/fuel ratio control      58
Approximate error covariance matrix      24 29—34 49 63
Artificial process-noise      48—50
Attentional filtering      80
Automatic relevance determination (ARD)      205
Automotive applications      57
Automotive powertrain control systems      57
Avoiding matrix inversions      46
Backpropagation      30 39 44 51 56
Backpropagation process      55
Backward filtering      12
Bayes' rule      181
Bayesian methods      203
BPTT(h)      45
Cayley — Hamilton theorem      212
Central difference interpolation      230
Chaotic (dynamic) invariants      84
Chaotic dynamics      83
Cholesky factorization      11
Closed-loop controller      60
Closed-loop evaluation      88 93 100 108 115
colored      166
Comparison of chaotic invariances of Ikeda map      97
Comparison of chaotic invariances of Lorenz series      102
Comparison of chaotic invariants of logistic map      90
Comparison of chaotic invariants of sea clutter      114
Computational complexity      24 33 34 39 46 63
Conditional mean estimator      4
Constrained weights      51
Correlation dimension      84
Cortical feedback      80
Cost functions      64
Covariance matrix of the process noise      31 32
Cross-entropy      54
Decoupled extended Kalman filter (DEKF)      26 33 39 47
Decoupled extended Kalman filter (NDEKF) algorithm      69
DEKF algorithm      34
Delay coordinate method      86
Derivative calculations      43 56
Derivative matrices      31 34 38
Derivative matrix      30 31 33
Derivatives of network outputs      44
Divergence phenomenon      10
Double inverted pendulum      234
Dual EKF      213
Dual estimation      123 130 224 249
Dual Kalman      125
Dynamic pattern classifiers      62
Dynamic reconstruction      85
Dynamic reconstruction of the laser series      109
Dynamic reconstruction of the Lorenz series      101
Dynamic reconstruction of the noisy Ikeda map      98
Dynamic reconstruction of the noisy Lorenz series      105
EKF      see “Extended Kalman filter” 37 43 52 54 56 62
EKF procedure      28
Elliott sigmoid      53
EM algorithm      142
Embedding      211
Embedding delay      86
Embedding dimension      86
Engine misfire detection      61
Entropic cost function      54 55
Error covariance matrices      48
Error covariance matrix      26
Error covariance propagation      8
Error covariance update      49
Error vector      29—31 34 38 52
Estimation      124
Expectation-maximization (EM) algorithm      177 182
Extended Kalman filter (EKF)      16 24 123 182 221 227
Extended Kalman filter, summary of      19
Extended Kalman filter-recurrent multilayered perceptron      83
Extended Kalman filtering (EKF) algorithm      179
Factor analysis (FA)      193
Filtering      3
Forward filtering      12
Fully decoupled EKE      25 34
Gauss — Hermite quadrature rule      230
GEKF      see “Global EKE” 30 33 34 39 62
GEKF, decoupled EKE algorithm      25
Generative model      178
Givens rotations      49 50
Global EKE (GEKF)      24 26
Global EKF training      29
Global scaling matrix      29 31 38
Global sealing matrix $A_{k}$      34
Graphical models      178 179
Hidden variables      177
Hierarchical architecture      71
Identifiability      206
Idle speed control      59
Ikeda map      91
Inference      176
Innovations      7
Jensen's inequality      183
Joint EKF      213
Joint estimation      137
Joint extended Kalman filter      125
Kalman filter      1 5 177
Kalman filter, information formulation of      13
Kalman gain      6
Kalman gain matrices      34 38
Kalman gain matrix      29 30 31 33 49
Kaplan — York dimension      85
Kernel      192
Kolmogorov entropy      85
Laser intensity pulsations      106
Layer-decoupled EKF      34
Learning rate      31 32 48
Least-squares solution      42
Logistic map      87
Lorenz attractor      99
Lyapunov dimension      85
Lyapunov exponents      84
Mammalian neocortex      70
MAP estimation      135
Marginal estimation      140
Markov-chain Monte Carlo      258
Matrices $\mathbf{H}^i_{k}$      52
Matrix factorization lemma      48
Matrix inversion lemma      14
Matrix inversions      55 63
Matrix of derivatives      29
Maximum a posteriori (MAP)      135
Maximum-likelihood cost      140
Measurement covariance      30
Measurement equation      3
Measurement error covariance matrix      38
Mixture of factor analyzers (MFA)      193
MMSE estimator      225
Model selection      203
Modeling      124
Monte Carlo simulation      255
Moving object      80
Multistream      39 40
Multistream EKF      26 38
Multistream EKF training      63
Multistream Kalman recursion      42
Multistream training      34 36 45
Neurobiological foundations      70
Node-decoupled EKF      25 34 46
Node-decoupled extended Kalman filter (NDEKF) algorithm      69
Noise      166
Noisy Ikeda series      95
Noisy Lorenz series      103
Noisy time-series estimation      153 235
Non-rigid motion      80
Nonlinear dynamic modelling of real-world time series      106
Nonlinear dynamics      175
Nonstationarity      202
Occlusions      75 78
On-line learning      201
Open-loop evaluation      87 92 99 108 115
Optimal recursive estiation      224
Optimization with constraints      51
Optimum smoothing problem      11
Overfitting      204
Parameter estimation      223 240
Partial M-step      200
Particle filters      182 259
Perceptual foundations      70
Prediction      3 124
Prediction error      126
Priming length      37
Principles of orthogonality      4
Process equation      2
Process noise      29
Proposal distribution      254
Radial basis function (RBF) networks      188
Rauch — Tung — Striebel      15 25
Rauch — Tung — Striebel (RTS) smoother      11 17 180
Real-time-recurrent learning (RTRL)      25
Recency effect      36
Recency phenomenon      25 26
Reconstruction failures      119
Recurrent derivative      131 164
Recurrent multilayered perceptron (RMLP)      26 28 30 61 69
Recurrent multiplayer perceptron      69
Recurrent network      28 44 59
Recurrent neural networks      60 62 63
Recursive Least-Squares (RLS) algorithm      201
Rescaled extended Kalman recursion      31
Sea clutter data      113
Sensor-catalyst modeling      60
Sequential DEKF      47
Sequential importance sampling      255
Sequential update      47
Shape and motion perception      80
Signal-to-ratio (SER)      87
Simultaneous DEKF      47
Singular-value decomposition      46
Smoothing      3
Speech enhancement      157
Square-root filtering      10 48—50
Square-root UKF      273
Stability      210
Stability and robustness      118
State estimation      127 176 222
State-error vector      5
Sum of squared error      29 64
Summary of the Kalman filter      10
Summary of the Rauch — Tung — Striebel smoother      17
Taken's theorem      211
Takens embedding      86
Teacher forcing      42
Tracking      70
Training cost function      31
Trajectory length      37
Truncated backpropagation through time (BPTT(h)      25 37 44
Unscented filter      182
Unscented Kalman filter (UKF)      221 228 230
Unscented Kalman smoother      237
Unscented particle filter      254
Unscented transformation      228
Variance estimation      149
Variational approximations      210
Vehicle emissions estimation      62
Weather data      197
Weight estimation      128
Weighting matrix      31 32
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