Batch scheme recursive Hartley modulating functions identification of nonlinear continuous-time Hammerstein model

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In this contribution, a new batch scheme recursive Hartley modulating functions identification approach is developed to estimate the parameters of a nonlinear continuous-time Hammerstein model. The method is implemented by moving a fixed window size of time series data forward at each sampling instance. A new transformation is formulated for the Hartley modulating function (HMF) which is suitable for recursive Hartley spectra computations. Once the initial sequential batch data is measured, the algorithm computes the required input-output Hartley transforms then updates recursively the sequential Hartley transforms and spectra for each coming sample of input-output signals. Hence, this will update the regressand vector and regression matrix of the system HMF model. After that, a least squares algorithm is employed to estimate recursively parameters of the linear dynamic system and the static nonlinear element. The batch scheme recursive algorithm developed here offers significant reductions in the computation of numerical Hartley integration compared to the nonrecursive implementation of the HMF-method [4]. In this paper, the numerical Hartley integration is based on a stair-case approximation and updated as a fixed window size which is shifted one step forward every sampling instant. Simulation studies are provided to illustrate the performance of the proposed algorithm.