Chicken Swarm Kernel Particle Filter: A Structured Rejuvenation Approach with KLD-Efficient Sampling
This work provides a theoretical framework for understanding computational efficiency in adaptive particle filters, which is incremental as it builds on existing methods without broad empirical validation.
The paper investigates the interaction between Chicken Swarm Optimization-based particle rejuvenation and KLD-based adaptive sampling in particle filters, finding that the CSO-enhanced filter is expected to require a lower expected particle count to meet the same statistical error bound under simplified assumptions.
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.