Bayesian approximation for parameterized KALMAN filter for investigation and simulation of unknown noise variance trajectory following in state space models with different noise distributions

Abstract

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, Bayesian approach for approximation of variances in measurement noise with KALMAN filter is applied for estimation of the dynamical state and measurement data in discrete dynamical system. Detection of uncertainty and estimation of those can be done simultaneously with adaptive KALMAN filter. This algorithm at each step time estimates noise variance and state of system with KALMAN filter. Then, approximation is formed at each step separately and at each step sufficient statistics of the state and noise variances are computed with a fixed-point iteration of a KALMAN filter. For showing influence of variance in measurement data on algorithm different simulations is applied. First, effect of variance and its distribution on detection performance is simulated in KALMAN filter without Bayesian formulation. Then simulation is applied to KALMAN filter with ability of variance tracking of measurement data.in these simulations, influence of distribution of measurement data in each step is estimated and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.