Comparison of Discrete and Continuous State Estimation with Focus on Active Flux Scheme

This paper deals with the state estimation of non-linear stochastic dynamic systems, both continuous and discrete in time, with an emphasis on a numerical solution to the Bayesian relations by the point-mass filters. The filters for discrete-discrete and continuous-discrete state-space models are reviewed and a new highly accurate and fast active flux method is introduced and adapted for a continuous filter design. A wide set of the point-mass filters is compared in a numerical study together with a set of particle filters.