Bounds on Passive Tdoa Estimation in Mixtures

We consider the problem of Time Difference of Arrival (TDOA) estimation in mixtures, namely when several sources are received by several receivers, possibly with different delays and attenuations. Under the assumption that the sources are stationary Gaussian with known spectra (a semi-blind scenario), we derive the Cramér-Rao Lower Bound on the Mean Squared Error (MSE) in unbiased joint estimation of the delays and of the mixing coefficients. We then analyze the results, drawing conclusions on the effects of the different model parameters (mixing coefficients, delay differences, signal to noise ratio) on the resulting bound, pointing out essential differences from the classical cases of static mixtures (with no delays) on one hand, and of single-source TDOA estimation on the other hand.