Time-delay estimation in mixtures

We address the problem of passive blind estimation of time-delays for several mutually uncorrelated source signals received by a similar number of sensors. The mixtures at the receivers are modeled as unknown linear combinations of differently delayed versions of the source signals. The standard tools used in blind source separation (BSS) for either static or convolutive mixtures are inappropriate for this problem: The former is obviously under-parameterized, while the latter is overparameterized and poorly suited for accommodating pure fractional delays. Thus, in this paper we propose a, hybrid algorithm, wliicb uses a specially parameterized approximate joint diagonalization of spectral matrices to estimate the delays (as well as the unknown mixing coefficients). The joint diagonalization algorithm is an extension of the iterative "AC-DC" algorithm, previously proposed in the context of BSS with static mixtures. We provide analytic exprcssions for all required steps for the two sensors / two sources case, and demonstrate the perforniance using sirnulations results.