  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.
