Unbounded drift in the under-excited signed equation error adaptive identifier

An adaptive identification algorithm known as the signed error (SE) algorithm is considered. This algorithm involves modifying the classical least mean squares (LMS) algorithm through the introduction of a signum function in the prediction error multiplicand of the LMS update kernel. It is shown that certain classes of nonpersistently exciting regressors cause this algorithm to diverge even in the ideal noise-free environment. It is also shown that this divergence cannot occur if the rate at which the degree of persistent excitation decline is fast enough