Optimum Kernel Particle Filter For Asymmetric Laplace Noise

In this paper we present on-line Bayesian filtering methods for time series models corrupted by asymmetric Laplace noise. An optimum kernel particle filter is designed for the general asymmetric case, and its performance is compared to that of a traditional bootstrap filter and a newly designed Rao-Blackwellised particle filter for the symmetric linear case. The optimum kernel is shown to improve performance and reduce degeneracy in the filter for a non-linear time-series model, and both the Rao-Blackwellised and the optimum kernel filter show significant advantages over a traditional bootstrap particle filter for a linear model.