Min-Plus approaches and Cluster Based Pruning for Filtering in Nonlinear Systems

TL;DR

This paper presents a min-plus based filtering method for nonlinear systems that avoids linearization and introduces a clustering-based pruning technique to improve computational efficiency.

Contribution

It introduces a novel min-plus approach combined with cluster-based pruning for nonlinear filtering, enhancing computational feasibility without system linearization.

Findings

Effective filtering in nonlinear systems demonstrated

Clustering-based pruning improves computational efficiency

Avoids linearization of system dynamics

Abstract

The design of deterministic filters can be cast as a problem of minimizing an associated cost function for an optimal control problem. Employing the min-plus linearity property of the dynamic programming operator (associated with the control problem) results in a computationally feasible approach (while avoiding linearization of the system dynamics/output). This article describes the salient features of this approach and a specific form of pruning/projection, based on clustering, which serves to facilitate the numerical efficiency of these methods.