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For pseudo-linear regression identification models corresponding output error systems with colored measurement noises, a difficulty of identification is that there exist unknown inner variables and unmeasurable noise terms in the information vector. This paper presents an auxiliary model based multi-innovation stochastic gradient algorithm by using the auxiliary model technique and by expanding the scalar innovation to an innovation vector. Compared with single-innovation stochastic gradient algorithm, the proposed approach can generate highly accurate parameter estimates. The simulation results confirm theoretical findings.