Approximate Bayesian Prediction Using State Space Model with Uniform Noise

Abstract

This paper proposes a one-step-ahead Bayesian output predictor for the linear stochastic state space model with uniformly distributed state and output noises. A model with discrete-time inputs, outputs and states is considered. The model matrices and noise parameters are supposed to be known. Unknown states are estimated using the Bayesian approach. The complex polytopic support of the posterior probability density function (pdf) is approximated by a parallelotopic set. The state estimation consists of two stages, namely the time and data update including the mentioned approximation. The output prediction is performed as an interstep between the time update and the data update. The behaviour of the proposed algorithm is illustrated by simulations and compared with the Kalman filter.