From: MAUSAM (mausam_at_cs.washington.edu)
Date: Fri Apr 25 2003 - 11:17:02 PDT
This workshop tutorial discusses the various facets of Kalman filters. The
author discusses the stochastic state space models, equations governing
Kalman filters in linear domains, the extension of Kalman filters to
non-linear domains, and a simulated example where they could be useful.
In general, Kalman filters are applied in discrete linear stochastic
systems which have both system and measurement noise. The estimation of
the next state is fast because of recursive computation, i.e. the next
state only depends on the previous state and some noise model. In
particular one does not need to remember the complete history of states.
Kalman filters can be converted to Extended Kalman filters which can be
used for non-linear domains. The estimation process is linearized about
series expansion. Though not optimal, the authors mention that some of the
successful applications of Kalman filters come from non-linear domains.
Although the paper gives sufficient mathematical details and lots of
equations, the motivational real world examples are less frequent. The
authors give simulations on one particular example, however mention of
other places, these filters have been applied would have made the whole
discussion much more convincing.
Moreover, it would have been nice if the authors discussed the time
complexity of these computations and compared these with the
other existing techniques, both in terms of time taken and quality of
results produced.
It would be interesting to see how Kalman filters could be made relevant
to the different planning problems. One could think of using it in
resource planning to estimate the next state. A thought on finding
equivalences with Markov Models would improve my understanding of Kalman
filters.
This archive was generated by hypermail 2.1.6 : Fri Apr 25 2003 - 11:17:03 PDT