A novel adaptive time delay identification technique

In this work, a novel online adaptive time delay identification method is proposed for a class of signal processing and communication applications, where the received signal is a combination of the transmitted signal and its delayed forms with the delay values being uncertain and required to be estimated. The design relies on a filtered form of a prediction error-like term which is then used in the design of the novel nonlinear adaptive update law. The stability of the identification algorithm is then investigated via novel Lyapunov based tools and the time delay identification is proven to be globally uniformly ultimately bounded. Several numerical simulations are conducted to evaluate the performance of the proposed identifier where constant, slowly varying and suddenly changing delays are successfully identified even in the presence of additive noise.