Continuous-time adaptive filtering algorithms using sign operators

In this paper, we develop a continuous-time adaptive filtering algorithm. The use of continuous-time algorithms stems from the needs of treating problems with high sampling rates. Under the assumption of uniform mixing signals, we prove the convergence of the sign-regressor algorithm and derive its asymptotic normality. Representation of the asymptotic covariance is also derived. The stability of the algorithm is obtained via the use of Lyapunov function method. In addition, we demonstrate that the use of iterate averaging improves the asymptotic efficiency.