Approximate maximum likelihood delay estimation via orthogonal wavelet transform

A novel approximate maximum likelihood algorithm is proposed for estimating the time difference of arrival between signals received at two spatially s eparated sensors. Prior to cross correlation, one of the channel outputs is optimally weighted at different frequency bands with the use of an orthogo nal wavelet transform. It composes an array of multirate filters and is a t ime-domain implementation of the generalized cross correlation method. Howe ver, it does not suffer from the performance degradation due to the errors inherent in spectral estimation obtained from finite length data and is com putationally efficient. A simple decision rule is also provided to automati cally determine the requisite levels of wavelet decomposition. The effectiv eness of the method is demonstrated by comparing, with the direct cross cor relator, the Eckart processor and the Cramer-Rao lower bound (CRLB) for dif ferent noise conditions and wavelet filter lengths.