NCS: Kalman Filtering
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In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.
An Introduction to the Kalman Filter, G. Welch and G. Bishop
A New Approach to Linear Filtering and Prediction Problem, R.E. Kalman. Transactions of the ASME, Series D, 1960.