System identification based on variational Bayes method and the invariance under coordinate transformations

This paper proposes a parameter estimation method for state-space models based on the variational Bayes method. We adopt the same form of functions as the prior and posterior probability distributions so that we can be used it iteratively to obtain accurate estimation whereas the existing algorithms cannot be used iteratively. Furthermore, the proposed algorithm is invariant under coordinate transformations, in the sense that the posterior probabilities of state-space models similar to each other are equivalent. Moreover, a numerical example demonstrates the effectiveness of the proposed method.