References & Further Reading
References
- R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, 1960
The original Kalman filter paper.
- R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, 1961
Continuous-time Kalman-Bucy filter.
- B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice Hall, 1979
The standard reference for the state-space approach to filtering.
- T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation, Prentice Hall, 2000
Unified innovations-geometric treatment of Wiener and Kalman filtering.
- A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970
Foundational nonlinear filtering text.
- S. J. Julier and J. K. Uhlmann, Unscented Filtering and Nonlinear Estimation, 2004
Definitive UKF reference.
- E. A. Wan and R. van der Merwe, The Unscented Kalman Filter for Nonlinear Estimation, 2000
Introduces UKF for state-space estimation.
- M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking, 2002
Standard tutorial on particle filtering.
- D. Simon, Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches, Wiley, 2006
Accessible textbook treatment with worked examples.
- S. Särkkä, Bayesian Filtering and Smoothing, Cambridge University Press, 2013
Modern unified Bayesian view of Kalman-family algorithms.
- L. A. McGee and S. F. Schmidt, Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry, 1985
Historical account of the Apollo guidance application.
- M. B. Khalilsarai, Y. Song, S. Haghighatshoar, G. Caire, Structured Channel Covariance Estimation from Limited Samples in Massive MIMO, 2020
Further Reading
Extensions beyond the single-target linear-Gaussian setting.
Square-root and information-form Kalman filters
Kailath-Sayed-Hassibi, 'Linear Estimation,' Ch. 12-13
Numerically stable implementations that avoid forming $\mathbf{P}$ directly.
Rauch-Tung-Striebel smoother
Särkkä, 'Bayesian Filtering and Smoothing,' Ch. 8
Backward pass for computing $\hat{\mathbf{x}}[n|N]$ given the entire record.
Joint state-parameter estimation
Ljung, 'System Identification,' 2nd ed., 1999
EM and dual-Kalman schemes for identifying $(\mathbf{F},\mathbf{H},\mathbf{Q},\mathbf{R})$ online.