State estimation of nonlinear dynamical systems using nonlinear update based Unscented Gaussian Sum Filter

• We propose an alternate to UKF, called UGSF, that models the prior as a sum of Gaussians.
• The posterior weights in the UGSF algorithm are nonlinearly updated.
• The computational burden of UGSF is comparable to UKF.
• Implementation on two benchmark process examples shows superior performance of UGSF over UKF.
• A detailed derivation of the posterior density using Bayes’ rule is presented.

Two attractive features of Unscented Kalman Filter (UKF) are: (1) use of deterministically chosen points (called sigma points), and (2) only a linear dependence of the number of sigma points on the number of states. However, an implicit assumption in UKF is that the prior conditional state probability density and the state and measurement noise densities are Gaussian. To avoid the restrictive Gaussianity assumption, Gaussian Sum-UKF (GS-UKF) has been proposed in literature that approximates all the underlying densities using a sum of Gaussians. However, the number of sigma points required in this approach is significantly higher than in UKF, thereby making GS-UKF computationally intensive. In this work, we propose an alternate approach, labeled Unscented Gaussian Sum Filter (UGSF), for state estimation of nonlinear dynamical systems, corrupted by Gaussian state and measurement noises. Our approach uses a Sum of Gaussians to approximate the non-Gaussian prior density. A key feature of this approximation is that it is based on the same number of sigma points as used in UKF, thereby resulting in similar computational complexity as UKF. We implement the proposed approach on two nonlinear state estimation case studies and demonstrate its utility by comparing its performance with UKF and GS-UKF.