Discrete-time Stochastic Systems
Estimation and Control
(Sprache: Englisch)
Each chapter has exercises at the end for self study and the answers to many of these are included in an appendix.
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Produktinformationen zu „Discrete-time Stochastic Systems “
Each chapter has exercises at the end for self study and the answers to many of these are included in an appendix.
Klappentext zu „Discrete-time Stochastic Systems “
Discrete-time Stochastic Systems gives a comprehensive introduction to the estimation and control of dynamic stochastic systems and provides complete derivations of key results such as the basic relations for Wiener filtering. The book covers both state-space methods and those based on the polynomial approach. Similarities and differences between these approaches are highlighted. Some non-linear aspects of stochastic systems (such as the bispectrum and extended Kalman filter) are also introduced and analysed. The books chief features are as follows: inclusion of the polynomial approach provides alternative and simpler computational methods than simple reliance on state-space methods; algorithms for analysis and design of stochastic systems allow for ease of implementation and experimentation by the reader; the highlighting of spectral factorization gives appropriate emphasis to this key concept often overlooked in the literature; explicit solutions of Wiener problems are handy schemes, well suited for computations compared with more commonly available but abstract formulations; complex-valued models that are directly applicable to many problems in signal processing and communications. Changes in the second edition include: additional information covering spectral factorisation and the innovations form; the chapter on optimal estimation being completely rewritten to focus on a posterior estimates rather than maximum likelihood; new material on fixed lag smoothing and algorithms for solving Riccati equations are improved and more up to date; new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control. Discrete-time Stochastic Systems is primarily of benefit to students taking M.Sc. courses in stochastic estimation and control, electronic engineering and signal processing but may also be of assistance for self study and as a reference.
Discrete-time Stochastic Systems gives a comprehensive introduction to the estimation and control of dynamic stochastic systems and provides complete derivations of key results such as the basic relations for Wiener filtering. The book covers both state-space methods and those based on the polynomial approach. Similarities and differences between these approaches are highlighted. Some non-linear aspects of stochastic systems (such as the bispectrum and extended Kalman filter) are also introduced and analysed. The books chief features are as follows: inclusion of the polynomial approach provides alternative and simpler computational methods than simple reliance on state-space methods; algorithms for analysis and design of stochastic systems allow for ease of implementation and experimentation by the reader; the highlighting of spectral factorization gives appropriate emphasis to this key concept often overlooked in the literature; explicit solutions of Wiener problems are handy schemes, well suited for computations compared with more commonly available but abstract formulations; complex-valued models that are directly applicable to many problems in signal processing and communications. Changes in the second edition include: additional information covering spectral factorisation and the innovations form; the chapter on optimal estimation being completely rewritten to focus on a posterior estimates rather than maximum likelihood; new material on fixed lag smoothing and algorithms for solving Riccati equations are improved and more up to date; new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control. Discrete-time Stochastic Systems is primarily of benefit to students taking M.Sc. courses in stochastic estimation and control, electronic engineering and signal processing but may also be of assistance for self study and as a reference.
Inhaltsverzeichnis zu „Discrete-time Stochastic Systems “
1. Introduction1.1 What is a Stochastic System?
- Bibhography
2. Some Probability Theory
2.1 Introduction
2.2 Random Variables and Distributions
2.2.1 Basic Concepts
2.2.2 Gaussian Distributions
2.2.3 Correlation and Dependence
2.3 Conditional Distributions
2.4 The Conditional Mean for Gaussian Variables
2.5 Complex-Valued Gaussian Variables
2.5.1 The Scalar Case
2.5.2 The Multivariable Case
2.5.3 The Rayleigh Distribution
- Exercises
3. Models
3.1 Introduction
3.2 Stochastic Processes
3.3 Markov Processes and the Concept of State
3.4 Covariance Function and Spectrum
3.5 Bispectrum
3.A Appendix. Linear Complex-Valued Signals and Systems
3.A.1 Complex-Valued Model of a Narrow-Band Signal
3.A.2 Linear Complex-Valued Systems
3.B Appendix. Markov Chains
- Exercises
4. Analysis
4.1 Introduction
4.2 Linear Filtering
4.2.1 Transfer Function Models
4.2.2 State Space Models
4.2.3 Yule-Walker Equations
4.3 Spectral Factorization
4.3.1 Transfer Function Models
4.3.2 State Space Models
4.3.3 An Example
4.4 Continuous-time Models
4.4.1 Covariance Function and Spectra
4.4.2 Spectral Factorization
4.4.3 White Noise
4.4.4 Wiener Processes
4.4.5 State Space Models
4.5 Sampling Stochastic Models
4.5.1 Introduction
4.5.2 State Space Models
4.5.3 Aliasing
4.6 The Positive Real Part of the Spectrum
4.6.1 ARMA Processes
4.6.2 State Space Models
4.6.3 Continuous-time Processes
4.7 Effect of Linear Filtering on the Bispectrum
4.8 Algorithms for Covariance Calculations and Sampling
4.8.1 ARMA Covariance Function
4.8.2 ARMA Cross-Covariance Function
4.8.3 Continuous-Time Covariance Function
4.8.4 Sampling
4.8.5 Solving the Lyapunov Equation
4. A Appendix. Auxiliary Lemmas
- Exercises
5. Optimal Estimation
5.1 Introduction
5.2 The Conditional Mean
5.3 The Linear Least Mean Square Estimate
5.4 Propagation of the Conditional Probability Density Function
5.5 Relation to Maximum Likelihood Estimation
5.A Appendix. A Lemma for
... mehr
Optimality of the Conditional Mean
- Exercises
6. Optimal State Estimation for Linear Systems
6.1 Introduction
6.2 The Linear Least Mean Square One-Step Prediction and Filter Estimates
6.3 The Conditional Mean
6.4 Optimal Filtering and Prediction
6.5 Smoothing
6.5.1 Fixed Point Smoothing
6.5.2 Fixed Lag Smoothing
6.6 Maximum a posteriori Estimates
6.7 The Stationary Case
6.8 Algorithms for Solving the Algebraic Riccati Equation
6.8.1 Introduction
6.8.2 An Algorithm Based on the Euler Matrix
6.A Appendix. Proofs
6.A.1 The Matrix Inversion Lemma
6.A.2 Proof of Theorem 6.1
6.A.3 Two Determinant Results
- Exercises
7. Optimal Estimation for Linear Systems by Polynomial Methods
7.1 Introduction
7.2 Optimal Prediction
7.2.1 Introduction
7.2.2 Optimal Prediction of ARMA Processes
7.2.3 A General Case
7.2.4 Prediction of Nonstationary Processes
7.3 Wiener Filters
7.3.1 Statement of the Problem
7.3.2 The Unrealizable Wiener Filter
7.3.3 The Realizable Wiener Filter
7.3.4 Illustration
7.3.5 Algorithmic Aspects
7.3.6 The Causal Part of a Filter, Partial Fraction Decomposition and a Diophantine Equation
7.4 Minimum Variance Filters
7.4.1 Introduction
7.4.2 Solution
7.4.3 The Estimation Error
7.4.4 Extensions
7.4.5 Illustrations
7.5 Robustness Against Modelling Errors
- Exercises
8. Illustration of Optimal Linear Estimation
8.1 Introduction
8.2 Spectral Factorization
8.3 Optimal Prediction
8.4 Optimal Filtering
8.5 Optimal Smoothing
8.6 Estimation Error Variance
8.7 Weighting Pattern
8.8 Frequency Characteristics
- Exercises
9. Nonlinear Filtering
9.1 Introduction
9.2 Extended Kaiman Filters
9.2.1 The Basic Algorithm
9.2.2 An Iterated Extended Kalman Filter
9.2.3 A Second-order Extended Kalman Filter
9.2.4 An Example
9.3 Gaussian Sum Estimators
9.4 The Multiple Model Approach
9.4.1 Introduction
9.4.2 Fixed Models
9.4.3 Switching Models
9.4,4 Interacting Multiple Models Algorithm
9.5 Monte Carlo Methods for Propagating the Conditional Probability Density Functions
9.6 Quantized Measurements
9.7 Median Filters
9.7.1 Introduction
9.7.2 Step Response
9.7.3 Response to Sinusoids
9.7.4 Effect on Noise
9.A Appendix. Auxiliary results
9.A.1 Analysis of the Sheppard Correction
9.A.2 Some Probability Density Functions
- Exercises
10. Introduction to Optimal Stochastic Control
10.1 Introduction
10.2 Some Simple Examples
10.2.1 Introduction
10.2.2 Deterministic System
10 2 3 Random Time Constant
10.2.4 Noisy Observations
10 2 5 Process Noise
10.2.6 Unknown Time Constants and Measurement Noise
10 2 7 Unknown Gain
10.3 Mathematical Preliminaries
10.4 Dynamic Programming
10.4.1 Deterministic Systems
10.4.2 Stochastic Systems
10.5 Some Stochastic Controllers
10.5.1 Dual Control
10.5.2 Certainty Equivalence Control
10.5.3 Cautious Control
- Exercises
11. Linear Quadratic Gaussian Control
11.1 Introduction
11.2 The Optimal Controllers
11.2.1 Optimal Control of Deterministic Systems
11.2.2 Optimal Control with Complete State Information
11.2.3 Optimal Control with Incomplete State Information
11.3 Duality Between Estimation and Control
11.4 Closed Loop System Properties
114 1 Representations of the Regulator
11.4.2 Representations of the Closed Loop System
11.4.3 The Closed Loop Poles
11.5 Linear Quadratic Gaussian Design by Polynomial Methods
11.5.1 Problem Formulation
11.5.2 Minimum Variance Control
11.5.3 The General Case
11.6 Controller Design by Linear Quadratic Gaussian Theory
11.6.1 Introduction
11.6.2 Choice of Observer Poles
11. A Appendix. Derivation of the Optimal Linear Quadratic Gaussian Feedback and the Riccati Equation from the Bellman Equation
- Exercises
- Answers to Selected Exercises
- Exercises
6. Optimal State Estimation for Linear Systems
6.1 Introduction
6.2 The Linear Least Mean Square One-Step Prediction and Filter Estimates
6.3 The Conditional Mean
6.4 Optimal Filtering and Prediction
6.5 Smoothing
6.5.1 Fixed Point Smoothing
6.5.2 Fixed Lag Smoothing
6.6 Maximum a posteriori Estimates
6.7 The Stationary Case
6.8 Algorithms for Solving the Algebraic Riccati Equation
6.8.1 Introduction
6.8.2 An Algorithm Based on the Euler Matrix
6.A Appendix. Proofs
6.A.1 The Matrix Inversion Lemma
6.A.2 Proof of Theorem 6.1
6.A.3 Two Determinant Results
- Exercises
7. Optimal Estimation for Linear Systems by Polynomial Methods
7.1 Introduction
7.2 Optimal Prediction
7.2.1 Introduction
7.2.2 Optimal Prediction of ARMA Processes
7.2.3 A General Case
7.2.4 Prediction of Nonstationary Processes
7.3 Wiener Filters
7.3.1 Statement of the Problem
7.3.2 The Unrealizable Wiener Filter
7.3.3 The Realizable Wiener Filter
7.3.4 Illustration
7.3.5 Algorithmic Aspects
7.3.6 The Causal Part of a Filter, Partial Fraction Decomposition and a Diophantine Equation
7.4 Minimum Variance Filters
7.4.1 Introduction
7.4.2 Solution
7.4.3 The Estimation Error
7.4.4 Extensions
7.4.5 Illustrations
7.5 Robustness Against Modelling Errors
- Exercises
8. Illustration of Optimal Linear Estimation
8.1 Introduction
8.2 Spectral Factorization
8.3 Optimal Prediction
8.4 Optimal Filtering
8.5 Optimal Smoothing
8.6 Estimation Error Variance
8.7 Weighting Pattern
8.8 Frequency Characteristics
- Exercises
9. Nonlinear Filtering
9.1 Introduction
9.2 Extended Kaiman Filters
9.2.1 The Basic Algorithm
9.2.2 An Iterated Extended Kalman Filter
9.2.3 A Second-order Extended Kalman Filter
9.2.4 An Example
9.3 Gaussian Sum Estimators
9.4 The Multiple Model Approach
9.4.1 Introduction
9.4.2 Fixed Models
9.4.3 Switching Models
9.4,4 Interacting Multiple Models Algorithm
9.5 Monte Carlo Methods for Propagating the Conditional Probability Density Functions
9.6 Quantized Measurements
9.7 Median Filters
9.7.1 Introduction
9.7.2 Step Response
9.7.3 Response to Sinusoids
9.7.4 Effect on Noise
9.A Appendix. Auxiliary results
9.A.1 Analysis of the Sheppard Correction
9.A.2 Some Probability Density Functions
- Exercises
10. Introduction to Optimal Stochastic Control
10.1 Introduction
10.2 Some Simple Examples
10.2.1 Introduction
10.2.2 Deterministic System
10 2 3 Random Time Constant
10.2.4 Noisy Observations
10 2 5 Process Noise
10.2.6 Unknown Time Constants and Measurement Noise
10 2 7 Unknown Gain
10.3 Mathematical Preliminaries
10.4 Dynamic Programming
10.4.1 Deterministic Systems
10.4.2 Stochastic Systems
10.5 Some Stochastic Controllers
10.5.1 Dual Control
10.5.2 Certainty Equivalence Control
10.5.3 Cautious Control
- Exercises
11. Linear Quadratic Gaussian Control
11.1 Introduction
11.2 The Optimal Controllers
11.2.1 Optimal Control of Deterministic Systems
11.2.2 Optimal Control with Complete State Information
11.2.3 Optimal Control with Incomplete State Information
11.3 Duality Between Estimation and Control
11.4 Closed Loop System Properties
114 1 Representations of the Regulator
11.4.2 Representations of the Closed Loop System
11.4.3 The Closed Loop Poles
11.5 Linear Quadratic Gaussian Design by Polynomial Methods
11.5.1 Problem Formulation
11.5.2 Minimum Variance Control
11.5.3 The General Case
11.6 Controller Design by Linear Quadratic Gaussian Theory
11.6.1 Introduction
11.6.2 Choice of Observer Poles
11. A Appendix. Derivation of the Optimal Linear Quadratic Gaussian Feedback and the Riccati Equation from the Bellman Equation
- Exercises
- Answers to Selected Exercises
... weniger
Bibliographische Angaben
- Autor: Torsten Söderström
- 2002, 2nd ed., XXII, 376 Seiten, 53 Abbildungen, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1852336498
- ISBN-13: 9781852336493
- Erscheinungsdatum: 26.07.2002
Sprache:
Englisch
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