Sequential Estimation of Hidden ARMA Processes by Particle Filtering-Part i

This paper is Part I of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we present estimation methods for ARMA processes of known model order, where the parameters are first known and then unknown. The driving noise of the ARMA process is Gaussian with unknown variance. We derive the transition density of the ARMA state for settings that correspond to different assumptions of a priori knowledge. Instead of estimating all the unknown parameters of the model, we treat them by Rao-Blackwellization. We propose a particle filtering method, with appropriate variations according to available information, for sequential estimation of the unknown state as it evolves with time. We demonstrate the performance of the proposed methods by extensive computer simulations.