Approximate Estimators for Linear Systems with Additive Cauchy Noises

The recently published optimal Cauchy estimator poses practical implementation challenges due to its time-growing complexity. Alternatively, addressing impulsive measurement and process noises, while using common estimation approaches, requires heuristic schemes. Approximate methods, such as particle and Gaussian-sum filters, were suggested to tackle the estimation problem in a heavy-tailed-noise environment when constraining the computational load. In this paper, the performances of a particle filter and a Gaussian-sum filter, designed for a linear system with specified Cauchy-noise parameters, are compared numerically to a Cauchy filter-based approximation showing the advantages of the latter.