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

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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… Click to show full abstract

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.

Keywords: model; gradient algorithm; two stage; auxiliary model

Journal Title: International Journal of Systems Science
Year Published: 2019

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