Trajectory-Induced Self-Calibration for Hidden-Target Localization Through an Unknown-Pose Range-Bearing Relay

• URL: http://arxiv.org/abs/2608.09464v1
• Date: Mon, 10 Aug 2026 11:34:24 GMT
• Title: Trajectory-Induced Self-Calibration for Hidden-Target Localization Through an Unknown-Pose Range-Bearing Relay
• Abstract summary: This paper studies hidden-target localization from range-bearing packets reported by a relay beacon whose global position and yaw are unknown.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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