Optimal Filtering of a Gaussian Signal in the Presence of Levy Noise

摘要

Many engineering applications require extracting a signal from observationscorrupted by additive noise, possibly heavy-tailed. We assume that the observation noise is a Levy process, while the signal is Gaussian, and derive a non-linear recursive filter that minimizes the L2 error. A sub-optimal filter is proposed for numerical purposes, and simulations show that it out performs the existing linear filter.