Moment-Based Prediction Step for Nonlinear Discrete-Time Dynamic Systems Using Exponential Densities

In this paper, an effcient approach for a moment-based Bayesian prediction step for both linear and nonlinear discrete-time dynamic systems using exponential densities with polynomial exponents is proposed. The exact solution of the prediction step is approximated by an exponential density which minimizes the Kullback-Leibler distance. Compared to other approaches, the user of this procedure can specify the approximation quality by controlling the deviation between the moments of the exact and the approximated solution. Furthermore, this algorithm can also be used for the adaptation of the order of the exponential densities either to improve the approximation quality or to reduce the computational effort.