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

• Published in: International journal of adaptive control and signal processing Vol. 31; no. 8; pp. 1184 - 1192
• Main Authors: Pavelková, Lenka, Jirsa, Ladislav
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.08.2017; Wiley Subscription Services, Inc
• Subjects: approximate parameter estimation; Approximation; ARX model; Autoregressive models; Autoregressive processes; Bayesian analysis; Bayesian estimation; bounded noise; Computer simulation; Kullback‐Leibler divergence; parallelotope; Parameter estimation; Recursive algorithms
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.2756

Summary 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.