The hybrid Cramer-Rao lower bound for simultaneous self-localization and room geometry estimation

This paper addresses the problem of tracking a moving source, e.g., a robot, equipped with both receivers and a source, that is tracking its own location and simultaneously estimating the locations of multiple plane reflectors. We assume a noisy knowledge of the robot's movement. We formulate this problem, which is also known as simultaneous localization and mapping (SLAM), as a hybrid estimation problem. We derive the extended Kalman filter (EKF) for both tracking the robot's own location and estimating the room geometry. Since the EKF employs linearization at every step, we incorporate a regulated kinematic model, which facilitates a successful tracking. In addition, we consider the echo-labeling problem as solved and beyond the scope of this paper. We then develop the hybrid Cramer-Rao lower bound on the estimation accuracy of both the localization and mapping parameters. The algorithm is evaluated with respect to the bound via simulations, which shows that the EKF approaches the hybrid Cramer-Rao bound (CRB) (HCRB) as the number of observation increases. This result implies that for the examples tested in simulation, the HCRB is an asymptotically tight bound and that the EKF is an optimal estimator. Whether this property is true in general remains an open question.

Automated summary

This paper addresses tracking a moving source equipped with both receivers and a source, formulating it as a hybrid estimation problem and deriving the extended Kalman filter (EKF). The algorithm's performance is evaluated through simulations, showing the EKF approaching the hybrid Cramer-Rao bound (HCRB) as the number of observations increases. This implies the EKF is an optimal estimator under certain conditions.