book

Model Identification and Data Analysis

Name: Model Identification and Data Analysis
Author: Sergio Bittanti
ISBN: 9781119546368

by Sergio Bittanti

April 2019

Beginner to intermediate

416 pages

12h 12m

English

Wiley

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Cover
Introduction
Acknowledgments
1 Stationary Processes and Time Series
1.1 Introduction1.2 The Prediction Problem1.3 Random Variable1.4 Random Vector1.5 Stationary Process1.6 White Process1.7 MA Process1.8 AR Process1.9 Yule–Walker Equations1.10 ARMA Process1.11 Spectrum of a Stationary Process1.12 ARMA Model: Stability Test and Variance Computation1.13 Fundamental Theorem of Spectral Analysis1.14 Spectrum Drawing1.15 Proof of the Fundamental Theorem of Spectral Analysis1.16 Representations of a Stationary Process
2 Estimation of Process Characteristics
2.1 Introduction2.2 General Properties of the Covariance Function2.3 Covariance Function of ARMA Processes2.4 Estimation of the Mean2.5 Estimation of the Covariance Function2.6 Estimation of the Spectrum2.7 Whiteness Test
3 Prediction
3.1 Introduction3.2 Fake Predictor3.3 Spectral Factorization3.4 Whitening Filter3.5 Optimal Predictor from Data3.6 Prediction of an ARMA Process3.7 ARMAX Process3.8 Prediction of an ARMAX Process
4 Model Identification
4.1 Introduction4.2 Setting the Identification Problem4.3 Static Modeling4.4 Dynamic Modeling4.5 External Representation Models4.6 Internal Representation Models4.7 The Model Identification Process4.8 The Predictive Approach4.9 Models in Predictive Form
5 Identification of Input–Output Models
5.1 Introduction5.2 Estimating AR and ARX Models: The Least Squares Method5.3 Identifiability5.4 Estimating ARMA and ARMAX Models5.5 Asymptotic Analysis5.6 Recursive Identification5.7 Robustness of Identification Methods5.8 Parameter Tracking
6 Model Complexity Selection
6.1 Introduction6.2 Cross‐validation6.3 FPE Criterion6.4 AIC Criterion6.5 MDL Criterion6.6 Durbin–Levinson Algorithm
7 Identification of State Space Models
7.1 Introduction7.2 Hankel Matrix7.3 Order Determination7.4 Determination of Matrices and 7.5 Determination of Matrix 7.6 Mid Summary: An Ideal Procedure7.7 Order Determination with SVD7.8 Reliable Identification of a State Space Model

8 Predictive Control
8.1 Introduction8.2 Minimum Variance Control8.3 Generalized Minimum Variance Control8.4 Model‐Based Predictive Control8.5 Data‐Driven Control Synthesis
9 Kalman Filtering and Prediction
9.1 Introduction9.2 Kalman Approach to Prediction and Filtering Problems9.3 The Bayes Estimation Problem9.4 One‐step‐ahead Kalman Predictor9.5 Multistep Optimal Predictor9.6 Optimal Filter9.7 Steady‐State Predictor9.8 Innovation Representation9.9 Innovation Representation Versus Canonical Representation9.10 K‐Theory Versus K–W Theory9.11 Extended Kalman Filter – EKF9.12 The Robust Approach to Filtering
10 Parameter Identification in a Given Model
10.1 Introduction10.2 Kalman Filter‐Based Approaches10.3 Two‐Stage Method
11 Case Studies
11.1 Introduction11.2 Kobe Earthquake Data Analysis11.3 Estimation of a Sinusoid in Noise
Appendix A: Linear Dynamical Systems
A.1 State Space and Input–Output ModelsA.2 Lagrange FormulaA.3 StabilityA.4 Impulse ResponseA.5 Frequency ResponseA.6 Multiplicity of State Space ModelsA.7 Reachability and ObservabilityA.8 System DecompositionA.9 Stabilizability and Detectability
Appendix B: Matrices
B.1 BasicsB.2 EigenvaluesB.3 Determinant and InverseB.4 RankB.5 Annihilating PolynomialB.6 Algebraic and Geometric MultiplicityB.7 Range and Null SpaceB.8 Quadratic FormsB.9 Derivative of a Scalar Function with Respect to a VectorB.10 Matrix Diagonalization via SimilarityB.11 Matrix Diagonalization via Singular Value DecompositionB.12 Matrix Norm and Condition Number
Appendix C: Problems and Solutions
Bibliography
Further reading
Index
End User License Agreement

Content preview from Model Identification and Data Analysis

9Kalman Filtering and Prediction

9.1 Introduction

In the first part of this book, we have treated the prediction problem for stationary processes as the problem of estimating the future value of a signal from the observation of its past snapshots. In other words, given the observations of , one is willing to find where . We now address a more general problem arising when the unknown variable may be different from the observed variable The estimation of is performed by taking advantage of the information on it hidden in through the relationship linking to , as expressed by a mathematical ...

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Model Identification and Data Analysis

by Sergio Bittanti

9Kalman Filtering and Prediction

9.1 Introduction

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