State-space modeling and estimation of time differences of arrival

Abstract

We propose a new method for time differences of arrival (TDOA's) estimation of multiple sources whose spectra are unknown. In the first part, we show how state-space techniques can be used to easily arrive at an exact discrete global model of the transfer between the source inputs and sensor outputs for sources having rational spectra and for integer and noninteger delays. This part is of interest by itself-e.g., for simulation purposes-but it also leads in a natural way to an original TDOA's estimation procedure presented in the second part of the paper. A condensed parametric model of the covariance information is the unique input to what can be seen as a generalized parametric covariance method. The difficulties inherent to these methods in the presence of several sources are easily turned around by a decoupling scheme which isolates the contributions of the individual, elementary sources. Simulation results are presented.