Two-stage multi-innovation stochastic gradient algorithm for multivariate output-error ARMA systems based on the auxiliary model

Qinyao Liu, Feng Ding, Quanmin Zhu and Tasawar Hayat

International Journal of Systems Science, 2019, vol. 50, issue 15, 2870-2884

Abstract: This paper investigates the parameter estimation problem for multivariate output-error systems perturbed by autoregressive moving average noises. Since the identification model has two different kinds of parameters, a vector and a matrix, the gradient algorithm cannot be used directly. Therefore, we decompose the original system model into two sub-models and proceed the identification problem by the collaboration between the two sub-models. By employing the gradient search and determining the optimal step-sizes, we present an auxiliary model based two-stage projection algorithm. However, in order to alleviate the sensitivity to the noise, we reselect the step-sizes and derive the auxiliary model based two-stage stochastic gradient (AM-2S-SG) algorithm. Based on the AM-2S-SG algorithm, an auxiliary model based two-stage multi-innovation stochastic gradient algorithm is proposed to generate more accurate estimates. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.

Date: 2019
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DOI: 10.1080/00207721.2019.1690720

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