On the impact of time-of-departure knowledge on the accuracy of time-of-arrival localization

We analyze the accuracy of source localization methods based on time-of-arrival (ToA) measurements from a set of cooperating receivers (anchors). We consider three different system scenarios, with and without knowledge of the time-of-departure (ToD) at the source. Our analysis is based on the formal derivation of the Cramér–Rao Bound (CRB) ellipsoids for each scenario. We analytically prove that an ordering relation is in place between the accuracy limits of the considered scenarios and provide insight about their geometric properties. The analysis reveals that the achievable accuracy depends on whether the source is inside or outside the anchors’ convex hull. The impact of ToD knowledge is very large outside the convex hull, but only modest inside. The presented analytic results bear concrete implications for practical system engineering.