A reduced-complexity and asymptotically efficient time-delay estimator

Abstract

This paper considers the problem of estimating the time delays of multiple replicas of a known signal received by an array of antennas. Under the assumptions that the noise and co-channel interference (CCI) are spatially colored Gaussian processes and that the spatial signatures are arbitrary, the maximum likelihood (ML) solution to the general time delay estimation problem is derived. The resulting criterion for the delays yields consistent and asymptotically efficient estimates. However, the criterion is highly non-linear, and not conducive to simple minimization procedures. We propose a new cost function that is shown to provide asymptotically efficient delay estimates. We also outline a heuristic way of deriving this cost function. The form of this new estimator lends itself to minimization by the computationally attractive iterative quadratic maximum likelihood (IQML) algorithm. The existence of simple yet accurate initialization schemes based on ESPRIT and identity weightings makes the approach viable for practical implementation.