Stochastic averaging analysis of an adaptive time delay estimation algorithm

The authors present a theoretical analysis of an adaptive delay estimation algorithm based on stochastic averaging theory. Both time-invariant and time-variant delay cases are considered. With time-invariant delay, the estimator is found to converge weakly to a deterministic differential equation as adaptive speed decreases. For the time-variant delay case, a first-order averaging analysis gives a similar result. Simulation results are also presented