Approximate maximum likelihood time-delay estimation for two closely spaced sources

Abstract

The study of ground reflections of Global Navigation Satellite System (GNSS) signals, as in GNSS Reflectometry (GNSS-R) can lead to the receiver height estimation. The latter is estimated by comparing the time of arrival difference between the direct and reflected signals, also called path separation. In ground-based scenarios, this path separation can be very small, inducing important interference between paths, which makes it difficult to correctly obtain altimetry products. The path separation estimation can be obtained by a brute force dual source maximum likelihood estimator (2S-MLE), but this solution has a large computational cost. On the other hand, the path separation is so small that a number of approximations can be done. In this study, a third order Taylor approximation of the dual source likelihood criterion is proposed to reduce its complexity. The proposed algorithm performance is compared to the non approximated 2S-MLE for the estimation of the path separation, and to a standard single source processing for the estimation of the direct signal time-delay. These results, along with the corresponding lower bounds, prove that the proposed approach may be of interest for two applications: ground-based GNSS-R altimetry (or radar with low elevation targets) and GNSS multipath mitigation.