# Improper Filter Reduction

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.

2 Amirkabir University of Technology

3 University of South Carolina

Abstract

Combinatorial filters, which are discrete representations of estimation
processes, have been the subject of increasing interest from the robotics
community in recent years.
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This paper considers automatic reduction of combinatorial filters to a given
size, even if that reduction necessitates changes to the filter's behavior.
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We introduce an algorithmic problem called \emph{improper
filter reduction}, in which the input is a combinatorial filter $F$ along
with an integer $k$ representing the target size.  The output is another
combinatorial filter $F'$ with at most $k$ states, such that the difference
in behavior between $F$ and $F'$ is minimal.
We present two methods for measuring the distance between pairs of filters, describe dynamic
programming algorithms for computing these distances, and
show that improper filter reduction is NP-hard under these methods.
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We then describe two heuristic algorithms for improper filter reduction, one
\changed{greedy sequential} approach, and one randomized global approach based on prior work
on weighted improper graph coloring.  We have implemented these algorithms
and analyze the results of three sets of experiments.

Keywords