Factorization Methods for Discrete Sequential Estimation (Dover Books on Mathematics)
Topics include a review of least squares data processing and the Kalman filter algorithm; positive definite matrices, the Cholesky decomposition, and some of their applications; Householder orthogonal transformations; sequential square root data processing; mapping effects and process noise; biases and correlated process noise; and covariance analysis of effects due to mismodeled variables and incorrect filter a priori statistics. The concluding chapters explore SRIF error analysis of effects due to mismodeled variables and incorrect filter a priori statistics as well as square root information smoothing. Geared toward advanced undergraduates and graduate students, this pragmatically oriented and detailed presentation is also a useful reference, featuring numerous helpful appendixes throughout the text.
Why Read This Book
You will learn how matrix factorization techniques produce numerically stable, efficient, and implementable sequential estimators — essential when Kalman filters suffer numerical breakdown in real systems. The book gives you a deep, practical grounding in square‑root and factorized algorithms (Cholesky, Householder, SRIF) so you can build robust estimators for radar, communications, audio/speech, and other signal‑processing applications.
Who Will Benefit
Engineers or researchers with an intermediate-to-advanced background in signal processing or controls who need to implement numerically reliable sequential estimation (Kalman/SRIF) in radar, navigation, communications, or audio systems.
Level: Advanced — Prerequisites: Linear algebra (matrix factorizations, positive definite matrices), basic probability and estimation theory, familiarity with least squares and the standard Kalman filter; programming experience for algorithm implementation (MATLAB/C/Python recommended).
Key Takeaways
- Apply Cholesky and Householder factorizations to derive numerically stable square‑root sequential estimators
- Implement sequential square‑root information and covariance filters (SRIF/SRCKF) for real‑time applications
- Analyze and quantify the effects of process noise, mapping, biases, and correlated noise on estimator covariance
- Diagnose and mitigate numerical instabilities and error growth in Kalman‑type filters using factorization methods
- Perform covariance analysis for mismodeled variables and incorrect a priori statistics to support robust design decisions
Topics Covered
- 1. Review of Least Squares and the Kalman Filter
- 2. Positive Definite Matrices and the Cholesky Decomposition
- 3. Orthogonal Transformations: Householder Methods
- 4. Sequential Square‑Root Data Processing: Theory and Algorithms
- 5. Square‑Root Information Filters (SRIF) and Implementations
- 6. Mapping Effects and Process Noise Modeling
- 7. Biases, Correlated Process Noise, and Their Treatment
- 8. Covariance Analysis for Mismodeled Variables and Incorrect A Priori Statistics
- 9. Numerical Stability, Error Propagation, and Practical Considerations
- 10. Examples and Applications: Navigation, Radar, and Communications Scenarios
- 11. Implementation Notes and Computational Economies
- 12. Appendices: Useful Identities, Algorithms, and Proofs
Languages, Platforms & Tools
How It Compares
More mathematically focused on matrix factorization and numerical stability than general Kalman texts such as Grewal & Andrews or Brown & Hwang; complements practical implementation guides like Simon's Optimal State Estimation by providing the factorization tools that make implementations robust.
