Particle filters with approximation steps

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. 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.