Improper Filter Reduction
Fatemeh Zahra Saberifar, Ali Mohades, Mohammadreza Razzazi and, Jason M.O'Kane

TL;DR
This paper introduces the problem of improper filter reduction, aiming to minimize behavioral differences when reducing combinatorial filters to a specified size, and presents algorithms and experimental analysis for this NP-hard problem.
Contribution
It formalizes improper filter reduction, proposes distance metrics, proves NP-hardness, and develops heuristic algorithms with experimental evaluation.
Findings
Improper filter reduction is NP-hard under proposed metrics.
Heuristic algorithms can effectively approximate minimal behavioral differences.
Experimental results demonstrate the algorithms' performance on various filter sets.
Abstract
Combinatorial filters 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 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 metrics 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 metrics. We then describe two heuristic algorithms for improper filter reduction, one greedy sequential approach, and…
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Taxonomy
TopicsDigital Filter Design and Implementation · Advanced Adaptive Filtering Techniques
