Introduction to Random Signals and Applied Kalman Filtering, 3rd Edition (Book only)
In this updated edition the main thrust is on applied Kalman filtering. Chapters 1-3 provide a minimal background in random process theory and the response of linear systems to random inputs. The following chapter is devoted to Wiener filtering and the remainder of the text deals with various facets of Kalman filtering with emphasis on applications. Starred problems at the end of each chapter are computer exercises. The authors believe that programming the equations and analyzing the results of specific examples is the best way to obtain the insight that is essential in engineering work.
Why Read This Book
You should read this book if you want a hands-on, engineering-focused introduction to random signals and state estimation: it walks you from the minimum random-process theory needed up through Wiener and Kalman filters and includes MATLAB exercises so you can translate theory into working code. The authors emphasize practical implementation issues (numerical conditioning, model tuning, smoothing) that you'll encounter in real DSP and tracking applications.
Who Will Benefit
Engineers or graduate students with basic signals/probability background who need to implement or understand Kalman and Wiener filtering for estimation, tracking, or signal-processing applications.
Level: Intermediate — Prerequisites: Undergraduate linear algebra, basic probability & random variables, signals and systems fundamentals, and familiarity with MATLAB for implementing exercises.
Key Takeaways
- Understand the fundamentals of random processes, autocorrelation, and power spectral density and how they affect linear systems
- Formulate and analyze Wiener filters for optimal linear estimation in the presence of noise
- Derive and implement discrete-time Kalman filters for linear state-space models
- Apply Kalman smoothing and fixed-interval/lag estimators to improve state estimates
- Address practical implementation issues such as numerical stability, covariance tuning, and model mismatch
- Translate Kalman and Wiener filter equations into working MATLAB code and run simulation exercises
Topics Covered
- 1. Introduction and Motivation
- 2. Basic Random Variables and Random Processes
- 3. Correlation, Power Spectra, and Linear Systems Driven by Random Inputs
- 4. Wiener Filtering and Optimal Linear Estimation
- 5. Discrete-Time State-Space Models and the Kalman Filter Derivation
- 6. Implementation Issues and Numerical Considerations
- 7. Kalman Smoothers and Fixed-Interval Estimation
- 8. Variations: Time-Varying Models and Practical Extensions
- 9. Applications in Tracking and Signal Processing
- 10. MATLAB Exercises and Starred Computer Problems
- Appendices: Linear Algebra, Probability Review, Miscellaneous Derivations
Languages, Platforms & Tools
How It Compares
More applied and exercise-oriented than Grewal & Andrews' 'Kalman Filtering: Theory and Practice Using MATLAB', and less comprehensive on modern nonlinear/advanced variants than Dan Simon's 'Optimal State Estimation'.
