**This textbook is intended for a graduate-level course and assumes familiarity with basic concepts from matrix theory, linear algebra, and linear system theory. Six appendices at the end of the book provide the reader with enough background and review material in all these areas.**

This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments in the new millennium. 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. The book also includes several results that appear in print for the first time.

*"synopsis" may belong to another edition of this title.*

This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments. This book contains a large collection of problems that complement it and are an important part of piece, in addition to numerous sections that offer interesting historical accounts and insights. The book also includes several results that appear in print for the first time.

**FEATURES/BENEFITS**

**Takes a geometric point of view.****Emphasis on the numerically favored array forms of many algorithms.****Emphasis on equivalence and duality concepts**for the solution of several related problems in adaptive filtering, estimation, and control.- These features are generally absent in most prior treatments, ostensibly on the grounds that they are too abstract and complicated. It is the authors' hope that these misconceptions will be dispelled by the presentation herein, and that the fundamental simplicity and power of these ideas will be more widely recognized and exploited. Among other things, these features already yielded new insights and new results for linear and nonlinear problems in areas such as adaptive filtering, quadratic control, and estimation, including the recent
*Hà theories*.

- These features are generally absent in most prior treatments, ostensibly on the grounds that they are too abstract and complicated. It is the authors' hope that these misconceptions will be dispelled by the presentation herein, and that the fundamental simplicity and power of these ideas will be more widely recognized and exploited. Among other things, these features already yielded new insights and new results for linear and nonlinear problems in areas such as adaptive filtering, quadratic control, and estimation, including the recent

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**Book Description **Prentice Hall, 2000. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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. Some Global Formulas. 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. Recursive Wiener Filtering 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 Alg. Bookseller Inventory # ABE_book_new_0130224642

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