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This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the parameter estimation problem of Hammerstein output error autoregressive (OEAR) systems. According to the maximum likelihood principle and the Levenberg–Marquardt optimization method, a maximum likelihood Levenberg–Marquardt recursive (ML-LM-R) algorithm using the varying interval input–output data is proposed. Furthermore, a stochastic gradient algorithm is also derived in order to compare it with the proposed ML-LM-R algorithm. Two numerical examples are provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]