An Improved Gaussian Sum Unscented Kalman Filter

Gaussian sum Unscented Kalman Filter (GS-UKF) is a recently improved estimator for state and parameter estimation of nonlinear dynamical systems. GS-UKF makes use of Unscented Kalman Filter (UKF) as a local filter at each of its individual Gaussians to obtain the local statistics. The UKF based local filters use a limited number of deterministically chosen samples, known as sigma points, to approximate the higher order moments of non-Gaussian prior. However, UKF has an inherent assumption of Gaussian statistics in approximation of non-Gaussian prior. This can undermines the true performance of UKF as well as GS-UKF. In this work, we propose to use Unscented Gaussian Sum Filter (UGSF), at each Gaussian of Gaussian Sum. UGSF uses the same UKF sigma points but approximates the prior with the sum of Gaussians, which can approximate any arbitrary density. We thus label our proposed approach as GS-UGSF. We show the utility of proposed GS-UGSF approach using a nonlinear case study from literature and compare the performance of GS-UGSF with GS-UKF.