Recursive Bayesian estimation of autoregressive model with uniform noise using approximation by parallelotopes

Abstract

This paper proposes a recursive algorithm for the estimation of a stochastic autoregressive model with an external input. The noise of the involved model is described by a uniform distribution. The model parameters are estimated using the Bayesian approach. Without an approximation, the support of the posterior distribution is a complex multidimensional polytope whose number of faces increases with time. We propose an approximation of this polytope in each time step by a parallelotope with a constant number of faces. The behaviour of the proposed algorithm is illustrated by simulations and compared with other methods. KEYWORDSapproximate parameter estimation, ARX model, Bayesian estimation, bounded noise, Kullback-Leibler divergence, parallelotope 1 1184

Zonotope and Gaussian Kalman filters based state estimation algorithm for linear system with dual noise term

“…The set-membership estimation method solves the optimal feasible set of states based on a set containing the true states of the system. The feasible set describing the state of the system can be described by different set spaces, such as intervals [12,13], ellipsoids [14,15], polytopes [16], and zonotopes [17,18]. The set-membership estimation method based on the interval has a regular shape, but its convergence speed is low.…”