Anchor-Free Hidden-Target Seeking via Certified Self-Calibration under Correlated Odometry

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.

A vehicle seeking a hidden target through a range-bearing relay of unknown position and yaw must decide, online, whether its own motion has already made the relay calibration trustworthy, and what to do when it has not. Two distinct vehicle-relative observations are known to remove the calibration gauge and make the target's relay-local packet globally actionable (arXiv:2608.09464), but that statement is static: it classifies a stored window only after the fact. This paper supplies the closed-loop layer: we show that the trajectory-spread margin $S_v$ that governs identifiability is simultaneously a finite-noise seed-accuracy bound, a local-vector variance decomposition, and a circle-geometry excitation budget, and we use it to supervise an excitation-reset controller. An excitation-supervised algorithm retriggers exploratory motion whenever the spread certificate is insufficient, projecting the target-seeking input away from the excitation's push, and otherwise proceeds to unrestricted target seeking. Under explicit sampling assumptions the supervision rule provably acquires any required excitation in finite time; in the noiseless local regime with positive excitation decay, estimator convergence yields target-seeking convergence after certification; and the threshold is selected from a desired calibration-accuracy level rather than chosen heuristically. Closed-loop simulation, paired Monte Carlo comparisons, a spread-threshold ablation, and a ROS 2/Gazebo software-in-the-loop experiment with sensing delay validate the approach. A decay-rate sweep shows that supervision matters when a fixed schedule's decay outruns the unknown time-to-adequate-excitation: over 100 paired trials the fixed baseline's yaw RMSE rises from 0.010 to 0.065 rad and success falls to 56%, while target-tracking error remains insensitive; supervision keeps yaw RMSE between 0.0095 and 0.0191 rad with 100% success.

Multi-camera pedestrian localization is useful for wide-area monitoring in public and commercial spaces. However, deploying these systems often requires considerable setup for each new environment. Existing methods typically require camera calibration, position annotations, or target-scene training. CAT-Free removes all three requirements. It uses synchronized RGB video as its only scene-specific input. Camera configuration is estimated directly from the video. Pedestrian locations are then estimated by combining observations from multiple cameras. Automatic camera estimation is not always accurate. This can produce unreliable pedestrian locations. CAT-Free therefore introduces two adaptive geometric filters. They remove unreliable position estimates. Their thresholds are estimated from each input sequence. CAT-Free achieves 82.5, 84.5, and 65.7 MODA on WildTrack, MultiviewX, and GMVD. It uses no supplied calibration, position annotations, or target-scene training. Published methods using such scene-specific information report 88.2--95.0 MODA on WildTrack and 83.9--96.5 on MultiviewX under their respective protocols. CAT-Free also transfers without retuning. It reaches 74.9 MODA on four additional sequences and 78.6 on an unseen 8-camera installation. Finally, localization uncertainty predicts MODA with $r=-0.98$. This provides a label-free estimate of localization reliability.