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

Many engineering applications require extracting a signal from observations corrupted 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 L error. A sub-optimal filter is proposed for numerical purposes, and simulations show that it out-performs the existing linear filter.