On Calculation of Bounds for Greedy Algorithms when Applied to Sensor Selection Problems

TL;DR

This paper analyzes the performance of greedy algorithms in sensor selection for stable linear systems with Kalman Filters, providing bounds and conditions for optimality based on system parameters.

Contribution

It develops an upper bound for the greedy algorithm's performance ratio and identifies conditions under which the greedy algorithm is guaranteed to be optimal.

Findings

Derived an upper bound for greedy algorithm performance ratio

Identified conditions for guaranteed optimality of greedy algorithms

Validated findings through simulations showing the impact of system parameters

Abstract

We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of greedy algorithms and conditions where greedy algorithm always produces optimal solutions. In this paper, we developed an upper bound for performance ratio of greedy algorithm, which is based on the work of Dr.Zhang \cite{Sundaram} and offers valuable insight into the system parameters that affects the performance of greedy algorithm. We also proposes a set of conditions where greedy algorithm will always produce the optimal solution. We then show in simulations how the system parameters mentioned by the performance ratio bound derived in this work affects the performance of greedy algorithm.