Fast and Robust Multivariate Estimator Based on Heavy-Tailed Cauchy Uncertainties

The multivariate Cauchy estimator (MCE) is an analytic and recursive state estimation algorithm derived using Bayes’s rule and applied to discrete-time dynamic systems. Unlike the Kalman filter, the MCE models its additive measurement and process noises as Cauchy distributed rather than Gaussian. Due to its complexity, the initially introduced MCE was limited to small-dimensional problems running for short time horizons. In this paper, we propose several enhancements to the MCE algorithm, which, when used collectively, yield a fast and robust multivariate estimation algorithm for linear and nonlinear dynamic systems of a moderate state-space dimension. These contributions allow, for the first time, the MCE to be tested in linear and nonlinear estimation applications. We demonstrate its advantages compared to the Extended Kalman Filter/unscented Kalman filter.