Periodic signals can be modeled as a real wave with unknown period in cascade with a piecewise linear function. A recursive Gauss-Newton prediction error method (RPEM) 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 Cramér-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.