From: Tal Shaked (tshaked_at_u.washington.edu)
Date: Fri Apr 25 2003 - 10:37:46 PDT
An Introduction to the Kalman Filter – G. Welch, G. Bishop
This paper describes in detail (at least relatively speaking) the
mathematics behind the Kalman filter, which is a technique used to estimate
(theoretically optimal in some cases) the state of some process by
repeatedly predicting states and then updating the analysis based on noisy
measurements.
The Kalman filter is a recursive data processing algorithm, which means that
it does not need to store all measurements when receiving and processing new
ones, making it fast and practical.
Theoretically the Kalman filter should work best on a process that can be
described by a linear model. However, the Extended Kalman Filter is
described which can estimate non-linear processes quite well through some
simplifications.
This paper assumed more background on the topic than I had. It was not
clear what exactly the problem was unless the person already knew or
actually took the advice and looked at Maybeck’s much friendlier
presentation.
It would be interesting to see how Kalman filters can/have been applied to
some specific/implemented planning systems. In cases where it is not
optimal, what conditions are necessary (and how likely are they) to cause it
to estimate poorly?
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