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For parameter estimation of output error moving average (OEMA) systems, this study combines the auxiliary model identification idea with the filtering theory, transforms an OEMA system into two identification models and presents a filtering and auxiliary model-based recursive least squares (F-AM-RLS) identification algorithm. Compared with the auxiliary model-based recursive extended least squares algorithm, the proposed F-AM-RLS algorithm has a high computational efficiency. Moreover, a filtering and auxiliary model-based least squares iterative (F-AM-LSI) identification algorithm is derived for OEMA systems with finite measurement input-output data. Compared with the F-AM-RLS approach, the proposed F-AM-LSI algorithm updates the parameter estimation using all the available data at each iteration, and thus can generate highly accurate parameter estimates.