Nonlinear filtering update phase via the single point truncated unscented Kalman filter

A fast algorithm to approximate the first two moments of the posterior probability density function (pdf) in nonlinear non-Gaussian Bayesian filtering is proposed. If the pdf of the measurement noise has a bounded support and the measurement function is continuous and bljective, we can use a modified prior pdf that meets Bayes' rule exactly. The central idea of this paper is that a Kalman filter applied to a modified prior distribution can improve the estimate given by the conventional Kalman filter. In practice, bounded support is not required and the modification of the prior is accounted for by adding an extra-point to the set of sigma-points used by the unscented Kalman filter.