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Résumé
This book contains a large collection of problems that complement the text and are an important part of it, in addition to numerous sections that offer interesting historical accounts and insights.
Contents
1. Overview.- The Asymptotic Observer.
- The Optimum Transient Observer.
- Coming Attractions.
- The Innovations Process.
- Steady-State Behavior.
- Several Related Problems.
- Complements.
- Problems.
2. Deterministic Least-Squares Problems.- The Deterministic Least-Squares Criterion.
- The Classical Solutions.
- A Geometric Formulation: The Orthogonality Condition.
- Regularized Least-Squares Problems.
- An Array Algorithm: The QR Method.
- Updating Least-Squares Solutions: RLS Algorithms.
- Downdating Least-Squares Solutions.
- Some Variations of Least-Squares Problems.
- Complements.
- Problems.
- On Systems of Linear Equations.
3. Stochastic Least-Squares Problems.- The Problem of Stochastic Estimation.
- Linear Least-Mean-Squares Estimators.
- A Geometric Formulation.
- Linear Models.
- Equivalence to Deterministic Least-Squares.
- Complements.
- Problems.
- Least-Mean-Squares Estimation.
- Gaussian Random Variables.
- Optimal Estimation for Gaussian Variables.
4. The Innovations Process.- Estimation of Stochastic Processes.
- The Innovations Process.
- Innovations Approach to Deterministic Least-Squares Problems.
- The Exponentially Correlated Process.
- Complements.
- Problems.
- Linear Spaces, Modules, and Gramians.
5. State-Space Models.- The Exponentially Correlated Process.
- Going Beyond the Stationary Case.
- Higher Order Processes and State-Space Models.
- Wide Sense Markov Processes.
- Complements.
- Problems.
- The Linear Model Induced by State-Space Models.
6. Innovations for Stationary Processes.- Innovations via Spectral Factorization.
- Signals and Systems.
- Stationary Random Processes.
- Canonical Spectral Factorization.
- Scalar Rational z-Spectra.
- Vector-Valued Stationary Processes.
- Complements.
- Problems.
- Continuous Time-Systems and Processes.
7. Wiener Theory for Scalar Processes.- Continuous-Time Wiener Smoothing.
- The Continuous-Time Wiener-Hopf Equation.
- Discrete-Time Problems.
- The Discrete Time Wiener-Hopf Technique.
- Causal Parts via Partial Fractions.
- Important Special Cases and Examples.
- Innovations Approach to the Wiener Filter.
- Vector Processes.
- Extensions of Wiener Filtering.
- Complements.
- Problems.
- The Continuous-Time Wiener-Hopf Technique.
8. Wiener-Kalman Theory in the Vector Case.- Time-Invariant State-Space Models.
- An Equivalence Class for Input Gramians.
- Canonical Spectral Factorization.
- Factorization Given Covariance Data.
- Predicted and Smoothed Estimators of the State.
- Extensions to Time-Variant Models.
- Complements.
- Problems.
- The Popov Function.
- System Theory Approach to Rational Spectral Factorization.
- The KYP and Bounded Real Lemmas.
- Vector Spectral Factorization in Continuous-Time.
9. The Kalman Filter.- The Standard State-Space Model.
- The Kalman Filter Recursions for the Innovations.
- Recursions for Predicted and Filtered State Estimators.
- Triangular Factorizations of Ry and Ry^-1.
- An Important Special Assumption: Ri >> 0.
- Covariance-Based Filters.
- Approximate Nonlinear Filtering.
- Backwards Kalman Recursions.
- Complements.
- Problems.
- Factorization of Ry Using the MGS Procedure.
- Factorization via Gramian Equivalence Classes.
10. Smoothed Estimators.- General Smoothing Formulas.
- Exploiting State-Space Structure.
- The Rauch-Tung-Striebel (RTS) Recursions.
- Two-Filter Formulas.
- The Hamiltonian Equations (Ri >> 0).
- Variational Origin of Hamiltonian Equations.
- Applications of Equivalence.
- Complements.
- Problems.
11. Fast Algorithms.- The Fast (CKMS) Algorithms.
- Two Important Cases.
- Structured Time-Variant Systems.
- CKMS Recursions given Covariance Data.
- Relation to Displacement Rank.
- Complements.
- Problems.
12. Array Algorithms.- Review and Notations.
- Potter's Explicit Algorithm for Scalar Measurement Update.
- Several Array Algorithms.
- Numerical Examples.
- Derivations of the Array Algorithms.
- A Geometric Explanation of the Arrays.
- Paige's Form of the Array Algorithm.
- Array Algorithms for the Information Forms.
- Array Algorithms for Smoothing.
- Complements.
- Problems.
- The UD Algorithm.
- The Use of Schur and Condensed Forms.
- Paige's Array Algorithm.
13. Fast Array Algorithms.- A Special Case: P0 = 0.
- A General Fast Array Algorithm.
- From Explicit Equations to Array Algorithms.
- Structured Time-Variant Systems.
- Complements.
- Problems.
- Combining Displacement and State-Space Structures.
14. Asymptotic Behavior.- Introduction.
- Solutions of the DARE.
- Summary of the Convergence Proofs.
- Riccati Solutions for Different Initial Conditions.
- Convergence Results.
- The Case of Stable Systems.
- The Case of S.O0.
- Exponential Convergence of the Fast Recursions.
- Complements.
- Problems.
15. Duality and Equivalence in Estimation and Control.- Dual Bases.
- Application to Linear Models.
- Duality and Equivalence Relationships.
- Duality Under Causality Constraints.
- Measurement Constraints and a Separation Principle.
- Duality in the Frequency Domain.
- Complementary State-Space Models.
- Complements.
- Problems.
16. Continuous-Time State-Space Estimation.- Continuous-Time Models.
- The Continuous-Time Kalman Filter Equations.
- Some Examples.
- Smoothed Estimators.
- Fast Algorithms for Time-Invariant Models.
- Asymptotic Behavior.
- Steady-State Filter.
- Complements.
- Problems.
- Backwards Markovian Models.
17. A Scattering Theory Approach.- A Generalized Transmission-Line Model.
- Backward Evolution.
- The Star Product.
- Various Riccati Formulas.
- Homogeneous Media: Time-Invariant Models.
- Discrete-Time Scattering Formulation.
- Further Work.
- Complements.
- Problems.
- A Complementary State-Space Model.
A. Useful Matrix Results.- Some Matrix Identities.
- Kronecker Products.
- The Reduced and Full QR Decompositions.
- The Singular Value Decomposition and Applications.
- Basis Rotations.
- Complex Gradients and Hessians.
- Further Reading.
B. Unitary and J-Unitary Transformations.- Householder Transformations.
- Circular or Givens Rotations.
- Fast Givens Transformations.
- J-Unitary Householder Transformations.
- Hyperbolic Givens Rotations.
- Some Alternative Implementations.
C. Controllability and Observability.- Linear State-Space Models.
- State-Transition Matrices.
- Controllabilty and Stabilizabilty.
- Observabilty and Detectabilty.
- Minimal Realizations.
D. Lyapunov Equations.- Discrete-Time Lyapunov Equations.
- Continuous-Time Lyapunov Equations.
- Internal Stability.
E. Algebraic Riccati Equations.- Overview of DARE.
- A Linear Matrix Inequality.
- Existence of Solutions to the DARE.
- Properties of the Maximal Solution.
- Main Result.
- Further Remarks.
- The Invariant Subspace Method.
- The Dual DARE.
- The CARE.
- Complements.
F. Displacement Structure.- Motivation.
- Two Fundamental Properties.
- A Generalized Schur Algorithm.
- The Classical Schur Algorithm.
- Combining Displacement and State-Space Structures.
- References.
Caractéristiques techniques
PAPIER | |
Éditeur(s) | Prentice Hall |
Auteur(s) | Thomas Kailath, Babak Hassibi, Ali H. Sayed |
Parution | 01/03/2000 |
Nb. de pages | 854 |
Format | 18,5 x 24 |
Couverture | Relié |
Poids | 1442g |
Intérieur | Noir et Blanc |
EAN13 | 9780130224644 |
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