Time delay estimation based on log-sum and l-norm penalized minor component analysis

Time-delay estimation (TDE), which measures the relative time delay between different receivers, is a fundamental approach for identifying, localizing, and tracking radiating sources. The generalized cross-correlation method is the most popular and is well explained in a landmark paper by Knapp and Carter [(1976). IEEE Trans. Acoust. Speech Signal Process. 24(4), 320-327]. Adaptive eigenvalue decomposition- (EVD) based algorithms have also been developed to improve TDE performance, especially in reverberant environments. This paper extends the adaptive EVD algorithm to utilize the sparsity in transfer channel between source and receivers. Two estimation algorithms based on the log-sum and l_p-norm penalized minor component analysis by excitatory and inhibitory learning rules is proposed. In addition, simulations with uncorrelated, correlated noise and reverberation for several signal-to-noise ratios are performed to show the improved estimation performance in noise and reverberation.