This paper discusses a novel method and check the effectiveness in combining deterministic generalized orthonormal basis filters (GOBF) with stochastic autoregressive moving average (ARMA) filters and its state space representation. The effectiveness of GOBF models can be improved by coupling an ARMA model in the presence of unmeasured disturbances. In this work particle swarm optimization (PSO) algorithm is used to determine the poles of GOBF filter.