Optimal Filtering (Dover Books on Electrical Engineering)
This graduate-level text augments and extends beyond undergraduate studies of signal processing, particularly in regard to communication systems and digital filtering theory. Vital for students in the fields of control and communications, its contents are also relevant to students in such diverse areas as statistics, economics, bioengineering, and operations research.
Topics include filtering, linear systems, and estimation; the discrete-time Kalman filter; time-invariant filters; properties of Kalman filters; computational aspects; and smoothing of discrete-time signals. Additional subjects encompass applications in nonlinear filtering; innovations representations, spectral factorization, and Wiener and Levinson filtering; parameter identification and adaptive estimation; and colored noise and suboptimal reduced order filters. Each chapter concludes with references, and four appendixes contain useful supplementary material.
Why Read This Book
You should read this book if you need a rigorous, mathematically precise treatment of optimal estimation and filtering: it takes you from the discrete-time Kalman filter through smoothing, spectral factorization, and innovations representations, with attention to computational issues. The text bridges theory and practice so you can both derive key results and implement robust estimators for communications, control, and signal-processing tasks.
Who Will Benefit
Graduate students, researchers, and practicing engineers in signal processing, communications, and control who need a deep understanding of Kalman filtering, smoothing, and related optimal-estimation methods.
Level: Advanced — Prerequisites: Linear algebra, probability and stochastic processes, basic signals & systems, and familiarity with linear system theory and matrices.
Key Takeaways
- Implement the discrete-time Kalman filter and understand its update and prediction recursions.
- Derive and apply fixed-interval smoothing algorithms (e.g., Rauch–Tung–Striebel) for improved estimates.
- Perform spectral factorization and develop Wiener and Levinson filter solutions from first principles.
- Analyze stability, convergence, and statistical properties of Kalman filters and innovations representations.
- Address computational and numerical issues in practical filter implementations.
- Apply parameter identification and adaptive estimation techniques within an optimal-filtering framework.
Topics Covered
- Introduction and mathematical preliminaries
- Linear systems and estimation background
- The discrete-time Kalman filter: derivation and interpretation
- Properties, stability, and convergence of Kalman filters
- Time-invariant filters and spectral factorization
- Innovations processes and Wiener–Levinson filtering
- Smoothing: fixed-interval and fixed-lag methods (RTS smoother)
- Computational aspects and numerical implementation
- Nonlinear filtering: extensions and approximations
- Parameter identification and adaptive estimation
- Applications in communications and control
- Appendices: supporting mathematics and proofs
Languages, Platforms & Tools
How It Compares
More rigorous and control-theory oriented than Gelb's Applied Optimal Estimation; overlaps with topics in Simon's Optimal State Estimation and Kay's Fundamentals of Statistical Signal Processing but places stronger emphasis on spectral factorization and innovations representations.
