Estimation of time differences of arrival by pole decomposition

Time differences of arrival (TDOA´s) of emitter wave fronts to a spatially distributed array of sensors can be used to determine the source location. In this paper, we suggest a new method of TDOA estimation for multiple unknown autoregressive moving average (ARMA) sources and additive noise that may be correlated between the sensors. We derive a theoretical formula that only uses the receiver cross spectra and the source poles for the TDOA determination. The poles are estimated by a least squares technique, and two methods are suggested for the estimation of the cross spectra which allow tradeoffs between computational complexity and accuracy. A new time delay model is derived and used to show the applicability of the methods for noninteger TDOA´s. Results from simulations illustrate the performance of the algorithm by Monte Carlo trials and compare it to the Cramer-Rao bound.