Nonlinear Measurement Update for Recursive Filtering Based on the Gauss von Mises Distribution

In conventional Kalman-based state estimation algorithms, there is an assumption that the uncertainties in the system state and measurements are Gaussian distributed. However, this Gaussian assumption ignores the periodic nature of angular or orientation quantities. In this paper, the Gauss von Mises (GVM) distribution model defined on a cylindrical manifold is employed, the Dirac mixture approximation method is extended to deal with sampling with GVM, in order to perform recursive filtering, the GVM approximation to joint distribution is proposed, the formula to compute posterior distribution is derived. Finally, the measurement update algorithm is developed. Simulation results show that when the system state contains a circular variable, the proposed GVM filter can achieve more accurate estimates than the traditional extended Kalmanfilter(EKF), thereby providing a novel method to estimate system state specialized to GVM distribution.