Maximum likelihood time delay estimation and Cramér-Rao bounds for multipath exploitation

In this paper, time delay estimation using the maximum likelihood principle is addressed for the multipath exploitation problem, and the corresponding Cramér-Rao bounds are derived. A single wideband radar, and a target in a known reflecting geometry are assumed. If the multipath is indeed detectable and resolvable, it is shown here that multipath exploitation, firstly, permits estimating the angle of arrival (AoA) of the target with a single sensor, and secondly, improves estimation accuracy of the direct path time delay. Both these are possible because the multipath´s time delay is a deterministic function of the time delay of the direct path as well as its AoA, as is demonstrated here. The multipath caused from reflections from surfaces yields virtual radar sensors observing the target from different aspects, thereby allowing AoA estimation.