High-resolution multi-path time delay estimation using 2D blind deconvolution in third order cross-moment domain

The cross-correlation is an effective tool for estimating a time delay between two signals. Unfortunately, in practical world, there always exist problems of multi-path time delay estimation (MTDE). The cross-correlation fails to deal with the MTDE case. In this paper, a novel technique for high-resolution multi-path time delay estimation (HMTDE) is proposed. The new method is based on 2D blind deconvolution and the slice selection on the third order cross-moment (TOCM) of the two signals. To get a high resolution estimation of the multi-path time delay, it is necessary to remove the component of transmitted signal. Instead of solving a one-dimensional blind deconvolution problem in original signals domain, the proposed method solves a two-dimensional blind deconvolution problem in their TOCM domain. It recovers a scaled and time-shifted version of the reflectivity sequence with the maximum time delay slices (MTDS) of TOCM of the reflectivities corresponding to the two signals. The only information of the transmitted signal needed in this method is its third order moment TOM, which can be estimated only using the two receive signals. It is well known that higher order statistics (HOS) carry more information and be insensitive to additive Gaussian noise than does the second order statistics (SOS). These properties lead to a robust and unique solution of HMTDE by using our TOCM based approach.