Introduction to random signal analysis and Kalman filtering
Focuses on applied Kalman filtering and its random signal analysis. Important to all control system and communication engineers, it emphasizes applications, computer software and associated sets of special computer problems to aid in tying together both theory and practice. Along with actual case studies, a diskette is included to enable readers to actually see how Kalman filtering works.
Why Read This Book
You should read this book if you want a practical bridge between random signal theory and working Kalman filter implementations: it shows how to model stochastic signals, derive both discrete- and continuous-time Kalman filters, and run real examples. The author emphasizes numerical issues, software exercises and case studies so you gain hands-on experience, not just abstract derivations.
Who Will Benefit
Engineers and graduate students in signal processing, communications, radar, or control who need to design and implement Kalman filters for real-world systems.
Level: Intermediate — Prerequisites: Linear algebra (matrix methods), basic probability and random processes, signals and systems fundamentals, and calculus.
Key Takeaways
- Derive discrete- and continuous-time Kalman filter equations from state-space and stochastic process principles.
- Model physical systems and measurement noise as random processes and compute their covariances and spectra.
- Implement Kalman filters with attention to numerical stability, initialization, and practical computer considerations.
- Analyze steady-state filter behavior and design optimal filters for time-invariant systems.
- Apply Kalman filtering to real case studies (navigation, radar, communications) and work through software exercises.
- Extend core ideas to nonlinear problems using approximate/extended filtering approaches.
Topics Covered
- Preface and Introduction
- Review of Probability and Random Processes
- Spectral Analysis and Linear Systems with Random Inputs
- State-Space Models for Stochastic Signals
- Derivation of the Discrete-Time Kalman Filter
- Continuous-Time Kalman Filtering and Equivalents
- Steady-State and Time-Invariant Filters
- Numerical Implementation and Computer Considerations
- Extensions: Nonlinear and Approximate (Extended) Kalman Filters
- Applications and Case Studies (navigation, radar, communications)
- Computer Problems and Software Examples (diskette materials)
- Appendices: Mathematical Background and Tables
Languages, Platforms & Tools
How It Compares
More application- and code-oriented than tutorial papers like Welch & Bishop's 'Introduction to the Kalman Filter'; less up-to-date on modern numerical methods and MATLAB tooling than Grewal & Andrews or Simon's 'Optimal State Estimation', but strong on foundational random-signal analysis and practical examples for its era.
