Document Type : Research Paper


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

2 Amirkabir University of Technology

3 University of South Carolina


Combinatorial filters, which are discrete representations of estimation
processes, have been the subject of increasing interest from the robotics
community in recent years.
This paper considers automatic reduction of combinatorial filters to a given
size, even if that reduction necessitates changes to the filter's behavior.
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.
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.