Linear Estimation
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 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 Weiner 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.
Why Read This Book
You will get a comprehensive, mathematically rigorous foundation in optimal linear estimation — from Wiener filtering and spectral factorization to the full Kalman filter and smoothing theory. The book combines clear theory, plentiful problems, and historical insight so you can both understand the proofs and apply estimation methods to real DSP and communications problems.
Who Will Benefit
Graduate students, researchers, and practicing engineers working on signal estimation, tracking, filtering, or statistical signal processing who need a deep, rigorous reference.
Level: Advanced — Prerequisites: Linear algebra, probability and stochastic processes, signals & systems (state-space familiarity recommended), and comfort with differential/difference equations.
Key Takeaways
- Derive and analyze Wiener and Kalman filters in discrete and continuous time
- Apply spectral factorization and the innovations approach to design optimal linear estimators
- Solve and interpret Riccati equations and understand stability/steady-state Kalman behavior
- Design and implement optimal smoothing and prediction algorithms for stochastic signals
- Formulate estimation problems in state-space form and assess estimator performance
Topics Covered
- Introduction and Historical Perspective
- Preliminaries: Probability, Processes, and Linear Systems
- Stationary Processes and Spectral Factorization
- Wiener Filtering and Prediction Theory
- State-Space Formulation of Estimation Problems
- Discrete-Time Kalman Filtering and the Riccati Equation
- Continuous-Time Filtering and Kalman--Bucy Theory
- The Innovations Approach and Orthogonality Principle
- Smoothing and Fixed-Interval Estimation
- Numerical and Implementation Issues; Steady-State Filters
- Extensions, Applications, and Historical Notes
- Problems and Worked Examples
How It Compares
More mathematically complete and historically informative than Dan Simon's 'Optimal State Estimation' (which is more application- and implementation-focused), and more modern and accessible than Jazwinski's classic 'Stochastic Processes and Filtering Theory'.
