Estimation of ARMA state processes by particle filtering

There are many practical signal processing settings where a state-space model consists of a state described by an ARMA process that is observed via non-linear functions of the state. In this paper, we propose a particle filtering method for sequentially estimating the ARMA process in the presence of unknown parameters. In the considered problem, we have static and dynamic unknowns, and we show how to handle the static parameters so that the estimation of the state process does not degrade with time. We propose a new particle filter that approximates the posterior of all the unknowns by a Gaussian distribution, in combination with a Monte Carlo approach to the Rao-Blackwellization of the static parameters. We demonstrate the performance of the proposed method by extensive computer simulations.