From: Parag (parag_at_cs.washington.edu)
Date: Fri Apr 25 2003 - 10:58:05 PDT
"An Introduction to the Kalman Filter", by Greg Welch and Gary
Bishop.
The paper talks about Kalman Filter which is one of the
best known tools for stochastic estimation from noisy
sensor measurements.
The main ideas in the paper are:
1. The Kamlan filter estimates a process by using a form of feeback
control - the filter estimates the process state at some time and
then obtains feedback in the form of noisy measurements, using
it to further improve the original estimate.
2. For the case, when the process can be described using linear stochastic
equations, for a certain definition of error and given a set of assumptions,
the Kamlan filter can be proved to optimal.
3. The filter can easily be extended to the case of the non-linear process,
where although not optimal, it can be used to make quite good predictions.
Although, the toy example that the authors give seems insightful into
the working of the filter, It would have been more motivating if the authors
had talked about how the filter is used in some of the real world applications.
One of the directions for future work could be - to analyze if the filter
could be extended to the case of continuous processes i.e. given the
state of the process at some previous time intervals, we want to estimate
the state of the system at a given time t. Though, I can not think of a
very good applications of this at the moment, but I am sure there would
be a lot of domains where it could be useful.
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