Periodic signals can be modeled as a real wave with unknown period in cascade with a piecewise linear function. In this report, a recursive Gauss-Newton prediction error identification algorithm for joint estimation of the driving frequency and the parameters of the nonlinear output function parameterized in a number of adaptively estimated grid points is introduced. The Cramer-Rao bound (CRB) is derived for the suggested algorithm. Numerical examples indicate that the suggested algorithm gives better performance than using fixed grid point algorithms and easily can be modified to track both the fundamental frequency variations and the time varying amplitude.
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