Progressive Gaussian filtering based on Dirac Mixture approximations

In this paper, we propose a progressive Gaussian filter, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a system of ordinary first-order differential equations (ODE) that is used for continuously tracking the true non-Gaussian posterior by its best matching Gaussian approximation. Calculating the required moments of the true posterior is performed based on corresponding Dirac Mixture approximations. The performance of the new filter is evaluated in comparison with state-of-the-art filters by means of a canonical benchmark example, the discrete-time cubic sensor problem.