AI summaryⓘ
The authors studied how to find a hidden target using signals from a relay beacon whose exact location and orientation are unknown. Their vehicle knows where it has moved but cannot see the target directly; instead, it gets range and direction data relative to itself and the hidden target through the relay. They found that just one vehicle position leaves too much uncertainty, but two different observations let them precisely estimate the relay’s position and orientation as well as the target’s location in a noise-free setup. Their method works well even with noise and some bad data, outperforming a basic estimation approach by a large margin. They also identified how the vehicle’s movement affects the quality of localization.
Hidden-target localizationRange-bearing measurementsRelay beaconSelf-calibrationYaw estimationTrajectory observabilityMonte Carlo evaluationExtended Kalman Filter (EKF)Huber weightingLocalization ambiguity
Abstract
This paper studies hidden-target localization from range-bearing packets reported by a relay beacon whose global position and yaw are unknown. The vehicle knows its own trajectory but never directly senses the target; the relay packet contains only local-frame range and bearing to the vehicle and to the hidden target. Unlike bearing-only network localization, relative-frame localization, and target-enclosing control, the target is neither directly observed in the vehicle frame nor treated as a node in a relative-sensing graph. The main result characterizes the minimal motion that removes the resulting calibration ambiguity: one vehicle pose leaves a continuous yaw/translation/target gauge, whereas two distinct vehicle-relative observations from one unknown-pose relay constructively determine relay yaw (modulo 2 pi), relay position, and the anchored target in the noiseless case. A local rank corollary, a shared-target multi-beacon extension, and a trajectory-spread conditioning lemma connect relay self-calibration to finite-window excitation and native range-bearing estimation. In Monte Carlo evaluation the estimator recovers the hidden target with 5.5 mm RMSE, five times below the 30 mm per-packet range noise and thirteen times more accurate than a naive EKF baseline; it converges to the same accuracy from 2 m target offsets and 2.4 rad yaw errors, and Huber weighting preserves millimeter accuracy under 10% outlier corruption that drops the unprotected estimator to a 0.10 success rate. Trajectory spread predicts estimator quality: the two weakly excited trajectories carry condition numbers above 100 with success rates of 0.82 and 0.70, while every well-excited trajectory attains full success.