From: Alexander Yates (ayates_at_cs.washington.edu)
Date: Fri Apr 25 2003 - 00:19:12 PDT
Review of "An Introduction to the Kalman Filter", by Greg Welch and Gary
Bishop.
The Kalman filter is a method for estimating the state of a discrete-time
process in which the state depends linearly on the prior state. It can be
extended to nonlinear functions by making local linear approximations.
Kalman filters make successive approximations to estimates of the state of a
system based on a sequence of noisy observations and knowledge about how the
system transforms from one time step to another. The filter is important
because it can be shown to be optimal, in the sense that it minimizes a
certain error function, under some strong assumptions, but it remains a good
estimator even in many situations the assumptions are violated. Second, it
is tractable to implement because the estimate of the state can be computed
from the a single previous state estimate and the current observation, so it
does not need to look at the entire state history.
Whoever texed this paper didn't realize that referencing an equation would
insert the word "equation" into the text, so the word appears twice in a row
very frequently.
It might be interesting to consider how to extend Kalman filters to
continuous-time processes (whatever they are). Also, there are probably
other interesting ways to do nonlinear functions besides the one presented
here.
Alex
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