NCS: Packet-based Estimation
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In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario. We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.
An Introduction to the Kalman Filter, G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.
Wikipedia: Kalman Filter A webpage that gives a proof and some applications.
A New Approach to Linear Filtering and Prediction Problem, R.E. Kalman. Transactions of the ASME, Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof.
The Kalman Filter, G. Welch and G. Bishop. A webpage with many links on Kalman filter.
Optimal Filtering, B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.