Joint state and parameter estimation for hidden wide-sense stationary ARMA processes under unknown noise

The wide-sense auto-regressive moving-average (ARMA) model is widely applied into varieties of fields. The unknown bounded parameter estimation of an ARMA model is an extremely vital research subject. Up to recent, most research is conducted with the known disturbing environment noise or the model of the known noise with the unknown variance. Actually the disturbing noise in the modern control system is really complex and unknown. To the best of our knowledge, less attention on the unknown boundary parameter estimation for the wide-sense stationary hidden ARMA process with unknown noise is paid. In this paper, a dual particle filter-based method to estimate the state and unknown bounded parameter jointly for the hidden wide-sense ARMA processes under the unknown noise is presented, which includes two steps. In the first step, the kernel smoothing particle filter algorithm is utilized to estimate the unknown bounded ARMA model parameter. And sufficient statistics based on Beta distribution is utilized to approach the posterior distribution of the parameter. In the second step, the particle filter algorithm is utilized to estimate the state of an ARMA model with the model parameter obtained in the first step. For the noise model is extremely unknown, the Gaussian mixture model is adopted to approach the posterior probability function in the EM algorithm. Simulation results verify the effectiveness of the proposed scheme.