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## Book Description

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title, including solutions for instructors, are available online at www.cambridge.org/9780521875127.

1. Cover
2. Half Title
3. Title Page
5. Contents
6. Preface
7. Notation and symbols
8. List of abbreviations
9. 1. Introduction
10. 2. Linear algebra
1. 2.1 Introduction
2. 2.2 Vectors
3. 2.3 Matrices
4. 2.4 Square matrices
5. 2.5 Matrix decompositions
6. 2.6 Linear least-squares problems
7. 2.7 Weighted linear least-squares problems
8. 2.8 Summary
11. 3. Discrete-time signals and systems
1. 3.1 Introduction
2. 3.2 Signals
3. 3.3 Signal transforms
4. 3.4 Linear systems
5. 3.5 Interaction between systems
6. 3.6 Summary
12. 4. Random variables and signals
1. 4.1 Introduction
2. 4.2 Description of a random variable
3. 4.3 Random signals
4. 4.4 Power spectra
5. 4.5 Properties of least-squares estimates
6. 4.6 Summary
13. 5. Kalman filtering
1. 5.1 Introduction
2. 5.2 The asymptotic observer
3. 5.3 The Kalman-filter problem
4. 5.4 The Kalman filter and stochastic least squares
5. 5.5 The Kalman filter and weighted least squares
6. 5.6 Fixed-interval smoothing
7. 5.7 The Kalman filter for LTI systems
8. 5.8 The Kalman filter for estimating unknown inputs
9. 5.9 Summary
14. 6. Estimation of spectra and frequency-response functions
1. 6.1 Introduction
2. 6.2 The discrete Fourier transform
3. 6.3 Spectral leakage
4. 6.4 The FFT algorithm
5. 6.5 Estimation of signal spectra
6. 6.6 Estimation of FRFs and disturbance spectra
7. 6.7 Summary
15. 7. Output-error parametric model estimation
1. 7.1 Introduction
2. 7.2 Problems in estimating parameters of an LTI state-space model
3. 7.3 Parameterizing a MIMO LTI state-space model
4. 7.4 The output-error cost function
5. 7.5 Numerical parameter estimation
6. 7.6 Analyzing the accuracy of the estimates
7. 7.7 Dealing with colored measurement noise
8. 7.8 Summary
16. 8. Prediction-error parametric model estimation
1. 8.1 Introduction
2. 8.2 Prediction-error methods for estimating state-space models
3. 8.3 Specific model parameterizations for SISO systems
4. 8.4 Qualitative analysis of the model bias for SISO systems
5. 8.5 Estimation problems in closed-loop systems
6. 8.6 Summary
17. 9. Subspace model identification
1. 9.1 Introduction
2. 9.2 Subspace model identification for deterministic systems
3. 9.3 Subspace identification with white measurement noise
4. 9.4 The use of instrumental variables
5. 9.5 Subspace identification with colored measurement noise
6. 9.6 Subspace identification with process and measurement noise
7. 9.7 Using subspace identification with closed-loop data
8. 9.8 Summary
18. 10. The system-identification cycle
1. 10.1 Introduction
2. 10.2 Experiment design
3. 10.3 Data pre-processing
4. 10.4 Selection of the model structure
5. 10.5 Model validation
6. 10.6 Summary
19. References
20. Index