Adaptive Fractional Delay Estimation without Lock-up

Gradient based algorithms for adaptive estimation of fractional time delay are known to suffer from lock-up phenomena to some extend. This is mainly due to errors in the gradient estimate which are on its term caused by interpolation errors. By studying the expected behavior of a class of stochastic descent algorithms, we are able to show that by replacing derivatives with finite differences, lock-up can be prevented. The approach is validated by deriving a robust estimator which combines subsample accuracy with excellent convergence properties in a computational efficient way.