The data filtering based generalized stochastic gradient parameter estimation algorithms for multivariate output-error autoregressive systems using the auxiliary model

Abstract

Parameter estimation has wide applications in one-dimensional and multidimensional signal processing and filtering. This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the data filtering technique and the auxiliary model identification idea, we derive a filtering based auxiliary model generalized stochastic gradient algorithm. The key is to choose an appropriate filter to filter the input-output data and to study a novel method to get the system model parameters and noise model parameters respectively. By employing the multi-innovation identification theory, a filtering based auxiliary model multi-innovation generalized stochastic gradient algorithm is proposed. Compared with the auxiliary model generalized stochastic gradient algorithm, the proposed algorithms can generate more accurate parameter estimates. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.