Analysis of error propagation in particle filters with approximation

TL;DR

This paper analyzes how approximation methods in particle filters affect error propagation, providing theoretical bounds and empirical insights for resource-constrained implementations.

Contribution

It introduces time-uniform error bounds for particle filters with approximation, including subsampling and parametric methods, supported by numerical experiments.

Findings

Derived exponential inequalities for error bounds

Validated theoretical results with numerical experiments

Identified impact of approximation on filter performance

Abstract

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.