Convergence of the RPEM as Applied to Harmonic Signal Modeling

Emad Abd-Elrady

October 2000

Abstract:

Arbitrary periodic signals can be estimated recursively by exploiting the fact that a sine wave passing through a static nonlinear function generates a spectrum of overtones. The estimated signal model is hence parameterized as a real wave with unknown period in cascade with a piecewise linear function. The driving periodic wave can be chosen depending on any prior knowledge. The performance of a recursive Gauss-Newton prediction error identification algorithm for joint estimation of the driving frequency and the parameters of the nonlinear output function is therefore studied. A theoretical analysis of local convergence to the true parameter vector as well as numerical examples are given. Furthermore, the Cramer-Rao bound (CRB) is calculated in this report.

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