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.