Maximum A Posteriori Estimation of Time Delay

Time-delay estimation (TDE) is an important topic of array signal processing for applications such as source localization and beam-forming. With a pair of sensors, the generalized cross correlation (GCC) method is widely used for TDE and the maximum-likelihood (ML) estimation can be considered as a GCC prefilter. Unfortunately, the ML estimation suffers from performance degradation due to the limitation of having only finite duration signals available for estimating source and noise power spectral densities. Also, its optimality is governed by the signal to noise ratio (SNR) and multipath environments. In this paper, we propose a method of Maximum a posteriori (MAP) estimation of time delay based on the ML estimation by modeling the prior probability of time delay. Experimental results show that the proposed method outperforms the conventional ML estimation. It also ourperforms the phase transform (PHAT) method with moderate SNR in multipath environments.