Overview

The optimal estimation problems for linear dynamic systems, and in particular for systems with after-effect, reduce to different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of a variational problem determines an optimal estimator. In addition, frequently the optimal algorithm for one noise model must operate under another, more complex assumption about noise. Hence, simplified algorithms must be used. It is important to evaluate the level of nonoptimality for the simplified algorithms. Since the original variational problems can be very difficult, the estimate of nonoptimality must be obtained without solving the original variational problem. In this text, guaranteed levels of nonoptimality for simplified estimation and control algorithms are constructed. To obtain these levels the duality theory for convex extremal problems is used. The book should be of interest to applied mathematicians, researchers and engineers who deal with estimation and control systems. The material, which requires a good knowledge of calculus, is also suitable for a two-semester graduate or postgraduate course.

Full Product Details

Author:   A.I. Matasov
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   458
Dimensions:   Width: 17.00cm , Height: 2.30cm , Length: 24.40cm
Weight:   1.730kg
ISBN:  

9780792352785

ISBN 10:   0792352785
Pages:   420
Publication Date:   31 January 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Guaranteed Parameter Estimation.- 1. Simplest Guaranteed Estimation Problem.- 2. Continuous Measurement Case.- 3. Linear Programming.- 4. Necessary and Sufficient Conditions for Optimality.- 5. Dual Problem and Chebyshev Approximation.- 6. Combined Model for Measurement Noise.- 7. Least-Squares Method in Guaranteed Parameter Estimation.- 8. Guaranteed Estimation with Anomalous Measurement Errors.- 9. Comments to Chapter 1.- 10. Excercises to Chapter 1.- 2. Guaranteed Estimation in Dynamic Systems.- 1. Lagrange Principle and Duality.- 2. Uncertain Deterministic Disturbances.- 3. Conditions for Optimality of Estimator.- 4. Computation of Estimators.- 5. Optimality of Linear Estimators.- 6. Phase Constraints in Guaranteed Estimation Problem.- 7. Comments to Chapter 2.- 8. Excercises to Chapter 2.- 3. Kalman Filter in Guaranteed Estimation Problem.- 1. Level of Nonoptimality for Kaiman Filter.- 2. Bound for the Level of Nonoptimality.- 3. Derivation of Main Result.- 4. Kaiman Filter with Discrete Measurements.- 5. Proofs for the Case of Discrete Measurements.- 6. Examples for the Bounds of Nonoptimality Levels.- 7. Comments to Chapter 3.- 8. Excercises to Chapter 3.- 4. Stochastic Guaranteed Estimation Problem.- 1. Optimal Stochastic Guaranteed Estimation Problem.- 2. Approximating Problem. Bound for the Level of Nonoptimality.- 3. Derivation of Main Result for Stochastic Problem.- 4. Discrete Measurements in Stochastic Estimation Problem.- 5. Examples for Stochastic Problems.- 6. Kaiman Filter under Uncertainty in Intensities of Noises.- 7. Comments to Chapter 4.- 8. Excercises to Chapter 4.- 5. Estimation Problems in Systems with Aftereffect.- 1. Pseudo-Fundamental Matrix and Cauchy Formula.- 2. Guaranteed Estimation in Dynamic Systems with Delay.- 3. Level of Nonoptimality in Stochastic Problem.- 4. Simplified Algorithms for Mean-Square Filtering Problem.- 5. Control Algorithms for Systems with Aftereffect.- 6. Reduced Algorithms for Systems with Weakly Connected Blocks.- 7. Comments to Chapter 5.- 8. Excercises to Chapter 5.

Reviews

'...very useful publication which gives a broad vision of the problem under discussion, giving a deep understanding of how to deal with uncertainty in estimation problems and how to organize the calculations. It may be recommended as a very good introduction and reference book for those who are interested in solving real-life applied problems of filtering and estimation.' IEEE Transactions on Automatic Control, 46:3 (2001) 'We recommend this monograph which provides a broad vision of the state estimation problem.' Automatica, 38 (2002)

...very useful publication which gives a broad vision of the problem under discussion, giving a deep understanding of how to deal with uncertainty in estimation problems and how to organize the calculations. It may be recommended as a very good introduction and reference book for those who are interested in solving real-life applied problems of filtering and estimation.' IEEE Transactions on Automatic Control, 46: 3 (2001) We recommend this monograph which provides a broad vision of the state estimation problem.' Automatica, 38 (2002)

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