Robust eckart filters for time delay estimation

Minimax or robust filters which optimize worst-case performance have been considered previously for matched and Wiener filtering. In this paper we show how similar ideas can be applied to obtain robust versions of one particular filter, the Eckart filter, for time delay estimation. The use of a robust filter can eliminate the requirement of estimation of the signal and noise power spectral densities (PSD´s) and cross PSD´s, robust filters being less sensitive in their performance to variations of the input PSD´s within specified classes of PSD´s. Explicit solutions for specific classes of PSD´s are derived, and several numerical examples and simulation results are given. Similar formulations for robust filters should also be possible for other types of filters used in time delay estimation.