Multipath exploited Bayesian and Cramér-Rao bounds for single-sensor target localization

In urban scenarios, radar returns consist of a direct path return along with multipath returns from signal reflections off surfaces such as building walls or floors. When multipath is resolvable, and given the knowledge of the geometry of the reflecting surfaces, it has recently been demonstrated that multipath returns create additional “virtual” radar sensors, thereby permitting target localization with a single radar sensor. The goal of this article is to determine theoretical variance lower bounds on how well a single-sensor system is able to localize a target in the presence of exploitable multipath and discuss several practical issues that arise in this context, including the multipath association problem, clutter, and the impact of wall roughness. Exploiting multipath, rather than viewing it strictly as a hindrance, is an emerging topic in the radar community whose potential is not yet fully understood. Towards this goal, we first derive the Cramér-Rao and the Bayesian Cramér-Rao bounds on target localization using a single-sensor which exploits resolvable multipath. For a wide class of radar-target geometries, functions termed multipath preservers are derived which indicate when multipath is physically observable in the radar returns; these functions assist in evaluating the potential of multipath exploitation in urban sensing. Given a reflecting geometry, the obtained lower bounds 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 that variance bounds on the location parameters improve with richer resolvable multipath generating mechanisms.