Maintaining Robot Localizability with Bayesian Cramér-Rao Lower Bounds

Accurate and real-time position estimates are cru-cial for mobile robots. This work focuses on ranging-based positioning systems, which rely on distance measurements between known points, called anchors, and a tag to localize. The topology of the network formed by the anchors strongly influences the tag's localizability, i.e., its ability to be accurately localized. Here, the tag and some anchors are supposed to be carried by robots, which allows enhancing the positioning accuracy by planning the anchors' motions. We leverage Bayesian Cramer-Rao Lower Bounds (CRLBs) on the estimates' covariance in order to quantify the tag's localizability. This class of CRLBs can capture prior information on the tag's position and take it into account when deploying the anchors. We propose a method to decrease a potential function based on the Bayesian CRLB in order to maintain the localizability of the tag while having some prior knowledge about its position distribution. Then, we present a new experiment highlighting the link between the localizability potential and the precision expected in practice. Finally, two real-time anchor motion planners are demonstrated with ranging measurements in the presence or absence of prior information about the tag's position.