On the Interaction Between Chicken Swarm Rejuvenation and KLD-Adaptive Sampling in Particle Filters

TL;DR

This paper explores the theoretical interaction between Chicken Swarm Optimization rejuvenation and KLD-adaptive sampling in particle filters, providing insights into their combined efficiency.

Contribution

It offers a simplified analytical framework to understand how CSO affects particle distribution and reduces the expected particle count needed for accuracy in PFs.

Findings

CSO rejuvenation tends to produce more concentrated particle distributions.

KLD sampling efficiency can be improved by CSO-induced contraction.

Theoretical analysis supports empirical observations of combined technique efficiency.

Abstract

Particle filters (PFs) are often combined with swarm intelligence (SI) algorithms, such as Chicken Swarm Optimization (CSO), for particle rejuvenation. Separately, Kullback--Leibler divergence (KLD) sampling is a common strategy for adaptively sizing the particle set. However, the theoretical interaction between SI-based rejuvenation kernels and KLD-based adaptive sampling is not yet fully understood. This paper investigates this specific interaction. We analyze, under a simplified modeling framework, the effect of the CSO rejuvenation step on the particle set distribution. We propose that the fitness-driven updates inherent in CSO can be approximated as a form of mean-square contraction. This contraction tends to produce a particle distribution that is more concentrated than that of a baseline PF, or in mathematical terms, a distribution that is plausibly more ``peaked'' in a majorization sense. By applying Karamata's inequality to the concave function that governs the expected bin occupancy in KLD-sampling, our analysis suggests a connection: under the stated assumptions, the CSO-enhanced PF (CPF) is expected to require a lower \emph{expected} particle count than the standard PF to satisfy the same statistical error bound. The goal of this study is not to provide a fully general proof, but rather to offer a tractable theoretical framework that helps to interpret the computational efficiency empirically observed when combining these techniques, and to provide a starting point for designing more efficient adaptive filters.