Joint State and Parameter Estimation for Stationary ARMA Model with Unknown Noise Model

The parameter estimation of a wide-sense auto-regressive moving-average (ARMA) model, which is widely applied into a variety of fields, is an extremely important research subject. Most research is conducted with the known driving environment noise or assuming that the driving noise consists unknown variance. Actually the driving noise is really complex in reality. Until now, less attention on parameter estimation for a wide-sense stationary hidden ARMA process with unknown noise is paid attention, although it is very common in the complex control system. The paper presents parameter estimation method for hidden wide-sense ARMA processes with the known model order. A dual particle filter-based method is adopted to estimate joint states and parameters. The method can be divided into two steps. The first step utilizes the particle filter algorithm to estimate the state of an ARMA model, then conduct the estimation of parameters in the PF algorithm on the basis of state estimation in the second step. For the noise model is extremely unknown, the Gaussian mixture model is adopted to approach the posterior probability function in the process of the above dual PF algorithm according to EM algorithm. Simulation results verify the effectiveness of the proposed scheme.