Model reduction for linear bayesian system identification

Bayesian estimation methods have been recently introduced in the system identification community. When applied in this context, they allow to estimate the unknown system in terms of its impulse response coefficients, thus returning a model with high (possibly infinite) McMillan degree. In this paper we discuss how these Bayesian estimation techniques can be equipped with a completely automatic model reduction procedure, in order to obtain a low McMillan degree model as a final estimate. Besides being more suitable for filtering and control applications, low-order models seem also to better capture the dynamics of the systems to be identified, as demonstrated by the extensive Monte Carlo experiments which are included in this paper.