Efficient Cauchy estimation via a pre-computational technique

An efficient technique for the state estimator for multi-dimensional linear dynamic systems with additive Cauchy distributed process noises and measurement noises is discussed. The characteristic function (CF) of the unnormalized conditional probability has been shown to be an analytic and recursive sum of terms composed of a coefficient function of the measurements times on exponential, whose argument has directions operating on the spectral vector. We uncover several fundamental properties of the CF, including the direction coalignment, term combination and reconstruction of the coefficient terms. Based on these properties, a pre-computational technique is developed to enhance the computational efficiency. Numerical simulations of a three-state system demonstrates the performance of the Cauchy estimator under both Cauchy noise environment and Gaussian noise environment, compared to the standard Kalman Filter.