From: Kevin Sikorski (kws_at_cs.washington.edu)
Date: Fri Apr 25 2003 - 09:24:02 PDT
An Introductino to the Kalman Filter
Greg Welch and Gary Bishop
Discrete Kalman filters provide a statistical approach to the continuous
state estimation problem.
The Main Points:
Kalman Filters are a robust solution to continuous state estimation.
Their feasibility comes from the fact that they recursively predict the
next state.
Kalman Filters can be extended to model non-linear processes too.
However, in their standard form, such EKFs are non-optimal.
Points to Improve on:
The meat of this paper was really just the equations describing how Kalman
Filters work. Some people (me for example) have difficulty getting an
intuitive understanding of things from just raw equations. Adding some
graphs or figures illustrating the relationship of the estimate with
respect to previous inputs would have helped my degree of understanding.
Some discussion of when Kalman Filters may not work would have been
helpful - the experiment presented only shows one example of when Kalman
Filters might work. Also, a comparison with other computationally simpler
tracking strategies (mean? mode? Particle Filters are much more
computationally-intensive in small dimensions, but they could be compared
too).
Future Research:
The section on Extended Kalman Filters admits that the EKF is often a good
estimator, it is not optimal. I did not track down the Julier and Uhlmann
reference cited in this paper, but if these researchers did not succede in
making EKFs optimal (though admittedly I didn't understand what would make
a KF 'optimal'), then this would be an important issue to resolve.
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