Time Evolution of the State Probability Density Function by Iterative Polynomial Chaos Expansion

An algorithm to estimate the state distribution of a initial value problem subject to random perturbations is proposed. The main contribution of this paper is the ability to handle state dependent probability density functions governing the state change. The task is handled by iteratively applying a generalized polynomial chaos expansion on the inverse cumulative distribution functions of the state and state change. The feasibility of the algorithm is demonstrated with a kinematic vehicle model and compared against a Monte-Carlo-Simulation.