Online Bayesian system identification in multivariate autoregressive models via message passing

Abstract

We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, the procedure yields posterior distributions for the autoregressive coefficients and noise precision parameters. The uncertainties regarding these estimates propagate into the uncertainties on predictions for future system outputs, and support online model evidence calculations. We test the procedure on an autoregressive system, demonstrating convergence empirically, and a double mass-spring-damper system, demonstrating competitive performance.