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Special Topic: An Introduction to Kalman Filter

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Stationary Processes and Discrete Parameter Markov Processes

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 293))

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Abstract

The Kalman filter is often heralded as among the most impactful mathematical concepts and algorithms of applied mathematics of the twentieth century. The basic mathematical theory is presented in this chapter, together with an often cited example to illustrate the nature of the computations required for estimation and prediction with the Kalman filter.

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Notes

  1. 1.

    Kalman (1960).

  2. 2.

    See Brockwell and Davis (1991): §12.2.

  3. 3.

    The succinct treatment presented here follows Lacey (2020).

  4. 4.

    For example, MATLAB has special packages for Riccati equation iteration of the type required by Theorem 25.1.

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Bhattacharya, R., Waymire, E. (2022). Special Topic: An Introduction to Kalman Filter. In: Stationary Processes and Discrete Parameter Markov Processes. Graduate Texts in Mathematics, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-031-00943-3_25

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