Characterizing persistent excitation for the sign-sign equation error identifier

Abstract The sign-sign (SS) algorithm is a computationally efficient adaptive identifier, often used in signal processing tasks. It is obtained by introducing signum functions on both the regressor and the prediction error multiplicands in the update kernel of the well-known LMS algorithm. This paper gives a deterministic persistent excitation condition on the regressor sequence which guarantees SS convergence. It also gives conditions under which SS may diverge, and discusses how these persistent excitation conditions may be verified through a finite amount of computations.

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