Bayesian and Cramér-Rao bounds for single sensor target localization via multipath exploitation

In urban scenarios, target localization may be achieved using a single sensor via multipath exploitation. The multipath generating mechanisms such as building walls creates virtual radar sensors aiding in localization. For a wide class of radar-target geometries, specialized functions termed multipath preservers are derived to ensure that multipath is physically observable in the radar returns, and therefore these functions assist in evaluating the potential of multipath exploitation in urban sensing. The single sensor system performance is studied by deriving the Cramér-Rao and the Bayesian Cramér-Rao bounds (BCRBs). Given a reflecting geometry, these lower bounds and multipath preservers allow the radar operator to anticipate blind spots, place confidence levels on the localization results, and permit sensor positioning to optimally aid in exploiting multipath for target localization. It is shown here that Cramér-Rao bounds (CRBs) on the location parameters improve with additional multipath.