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Kalman Filtering Neural Networks - Haykin S.

Kalman Filtering Neural Networks

Author: Haykin S.
Publishers: Wiley publishing
Year of publication: 2001
Number of pages: 202
ISBNs: 0-471-36998-5
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Download: kalmanfilteringneuralnetworks2001.pdf

Kalman Filtering and Neural Networks, Edited by Simon Haykin Copyright 2001 John Wiley Sons, Inc. ISBNs: 0-471-36998-5 (Hardback); 0-471-22154-6 (Electronic)
KALMAN FILTERING AND NEURAL NETWORKS
Edited by
Simon Haykin
Communications Research Laboratory, McMaster University, Hamilton, Ontario, Canada
A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY SONS, INC.
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
Designations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or ALL CAPITAL LETTERS. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration.
Copyright 2001 by John Wiley & Sons, Inc.. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008,
This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought.
ISBN 0-471-22154-6
This title is also available in print as ISBN 0-471-36998-5.
For more information about Wiley products, visit our web site at www.Wiley.com.
CONTENTS
Preface xi
Contributors xiii
1 Kalman Filters 1
Simon Haykin
1.1 Introduction / 1
1.2 Optimum Estimates / 3
1.3 Kalman Filter / 5
1.4 Divergence Phenomenon: Square-Root Filtering / 10
1.5 Rauch-Tung-Striebel Smoother / 11
1.6 Extended Kalman Filter / 16
1.7 Summary / 20 References / 20
2 Parameter-Based Kalman Filter Training:
Theory and Implementation 23
Gintaras V Puskorius and Lee A. Feldkamp
2.1 Introduction / 23
2.2 Network Architectures / 26
2.3 The EKF Procedure / 28
2.3.1 Global EKF Training / 29
2.3.2 Learning Rate and Scaled Cost Function / 31
2.3.3 Parameter Settings / 32
2.4 Decoupled EKF (DEKF) / 33
2.5 Multistream Training / 35
v
vi CONTENTS
2.5.1 Some Insight into the Multistream Technique / 40
2.5.2 Advantages and Extensions of Multistream Training / 42
2.6 Computational Considerations / 43
2.6.1 Derivative Calculations / 43
2.6.2 Computationally Efficient Formulations for Multiple-Output Problems / 45
2.6.3 Avoiding Matrix Inversions / 46
2.6.4 Square-Root Filtering / 48
2.7 Other Extensions and Enhancements / 51
2.7.1 EKF Training with Constrained Weights / 51
2.7.2 EKF Training with an Entropic Cost Function / 54
2.7.3 EKF Training with Scalar Errors / 55
2.8 Automotive Applications of EKF Training / 57
2.8.1 Air/Fuel Ratio Control / 58
2.8.2 Idle Speed Control / 59
2.8.3 Sensor-Catalyst Modeling / 60
2.8.4 Engine Misfire Detection / 61
2.8.5 Vehicle Emissions Estimation / 62
2.9 Discussion / 63
2.9.1 Virtues of EKF Training / 63
2.9.2 Limitations of EKF Training / 64
2.9.3 Guidelines for Implementation and Use / 64
References / 65
3 Learning Shape and Motion from Image Sequences 69
Gaurav S. Patel, Sue Becker, and Ron Racine
3.1 Introduction / 69
3.2 Neurobiological and Perceptual Foundations of our Model / 70
3.3 Network Description / 71
3.4 Experiment 1 / 73
3.5 Experiment 2 / 74
3.6 Experiment 3 / 76
3.7 Discussion / 77 References / 81
CONTENTS vii
4 Chaotic Dynamics 83
Gaurav S. Patel and Simon Haykin
4.1 Introduction / 83
4.2 Chaotic (Dynamic) Invariants / 84
4.3 Dynamic Reconstruction / 85
4.4 Modeling Numerically Generated Chaotic Time Series / 87
4.4.1 Logistic Map / 87
4.4.2 Ikeda Map / 91
4.4.3 Lorenz Attractor / 99
4.5 Nonlinear Dynamic Modeling of Real-World Time Series / 106
4.5.1 Laser Intensity Pulsations / 106
4.5.2 Sea Clutter Data / 113
4.6 Discussion / 119 References / 121
5 Dual Extended Kalman Filter Methods 123
Eric A. Wan and Alex T. Nelson
5.1 Introduction / 123
5.2 Dual EKF - Prediction Error / 126
5.2.1 EKF - State Estimation / 127
5.2.2 EKF - Weight Estimation / 128
5.2.3 Dual Estimation / 130
5.3 A Probabilistic Perspective / 135
5.3.1 Joint Estimation Methods / 137
5.3.2 Marginal Estimation Methods / 140
5.3.3 Dual EKF Algorithms / 144
5.3.4 Joint EKF / 149
5.4 Dual EKF Variance Estimation / 149
5.5 Applications / 153
5.5.1 Noisy Time-Series Estimation and Prediction / 153
5.5.2 Economic Forecasting - Index of Industrial Production / 155
5.5.3 Speech Enhancement / 157
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