Why Read This Book

You should read this book if you need a rigorous treatment of how Kalman filtering behaves when the process/model assumptions are badly violated and how to design estimators that tolerate large uncertainties. It shows you theory and design tools (including H-infinity/minimax ideas and practical computation techniques) that let you move beyond nominal Kalman filtering toward robust implementations for real-world signals and systems.

Who Will Benefit

Advanced engineers, researchers, and graduate students who design state estimators or signal processing algorithms and who face modeling uncertainty in applications such as navigation, radar, or communications.

Level: Advanced — Prerequisites: Good understanding of linear systems and state-space models, basic Kalman filter theory, probability and stochastic processes, linear algebra, and familiarity with control theory concepts (recommended: introductory robust control/H-infinity basics).

Key Takeaways

• Analyze the effect of model uncertainties and nonlinearities on Kalman filter performance and stability.
• Design robust state estimators using H-infinity, risk-sensitive, and minimax estimation frameworks.
• Formulate and solve practical robust-filter design problems using LMIs and computational tools.
• Extend robust filtering concepts from linear to certain nonlinear systems and discrete-time settings.
• Apply robust estimation methods to signal-processing problems where model mismatch is significant.

Topics Covered

1. 1. Introduction and Motivation: Kalman Filtering with Large Uncertainties
2. 2. Review of Kalman Filter and State-Space Representations
3. 3. Modeling Uncertainty and Nonlinearity in Signals and Systems
4. 4. Robust Estimation Frameworks: Minimax and Risk-Sensitive Approaches
5. 5. H-infinity Filtering: Theory and Interpretations
6. 6. Linear Matrix Inequalities and Computational Techniques for Robust Filters
7. 7. Discrete-Time Robust Filtering and Implementation Issues
8. 8. Extensions to Nonlinear Systems and Approximate Methods
9. 9. Performance Analysis and Robustness Bounds
10. 10. Applications and Numerical Examples (navigation, radar, communications)
11. 11. Conclusions, Open Problems and Further Reading

Languages, Platforms & Tools

How It Compares

More theory-focused on robustness than Grewal & Andrews' practical Kalman filter text; overlaps conceptually with robust-control treatments such as Zhou, Doyle & Glover but applied specifically to state estimation rather than full-controller synthesis.