From: Christophe Bisciglia (chrisrb_at_cs.washington.edu)
Date: Fri Apr 25 2003 - 10:49:45 PDT
Welch and Bishop An Introduction to the Kalman Filter
This paper provides an overview Kalman Filters (KF). KF provides a method
for estimating the state of discrete time models such that the current
approximation depends only on the previous.
The big ideas in my mind were the following. First, the fact that the
current state depends only on the prior leads to fast efficient
implementations. However, in order to make this work, the KF algorithm is
limited to linear processes . which is restrictive, but nevertheless,
still allows for a large class of processes to be estimated. The other
idea that I liked was the algorithms optimality with respect to minimizing
the estimated error.
My complaint with the paper was its reliance on the equations to provide
an .introduction. . I.d hate to see the actual explanation. I don.t have a
heavy statistical background, and I had a very hard time even pulling the
main points out. It would have been very helpful to have some more
abstract explanations with pretty pictures.
As far as open research goes, I resort to consider what would happen
without the simplifying assumptions. Could the KF algorithm work with
non-linear processes . it seems like not in its current form, but could
one come up with any form of a tweak, or a sample of previous states to
store that could facilitate approximation with reasonable space
requirements?
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