References & Further Reading

References

  1. R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, 1960

    The original Kalman filter paper.

  2. R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, 1961

    Continuous-time Kalman-Bucy filter.

  3. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Prentice Hall, 1979

    The standard reference for the state-space approach to filtering.

  4. T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation, Prentice Hall, 2000

    Unified innovations-geometric treatment of Wiener and Kalman filtering.

  5. A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970

    Foundational nonlinear filtering text.

  6. S. J. Julier and J. K. Uhlmann, Unscented Filtering and Nonlinear Estimation, 2004

    Definitive UKF reference.

  7. E. A. Wan and R. van der Merwe, The Unscented Kalman Filter for Nonlinear Estimation, 2000

    Introduces UKF for state-space estimation.

  8. 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.

  9. D. Simon, Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches, Wiley, 2006

    Accessible textbook treatment with worked examples.

  10. S. Särkkä, Bayesian Filtering and Smoothing, Cambridge University Press, 2013

    Modern unified Bayesian view of Kalman-family algorithms.

  11. 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.

  12. 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.