Weighted Group-K Consistent Set Maximization for Outlier Rejection of Azimuth-Elevation Measurements

Abstract

Reliable localization in robotics requires robust handling of sensor outliers, particularly in environments where acoustic or bearing measurements are noisy. We propose a replicator-dynamics-based approach for weighted group- k consistent set maximization (rGkCM) to identify the densest subsets of mutually consistent measurements in hypergraphs. To complement existing range-based consistency metrics, we introduce a k = 3 azimuth-elevation consistency check for bearing measurements to static landmarks. Our method efficiently identifies cliques in weighted k -uniform hypergraphs, leveraging the fitness of nodes to guide both pruning and recovery. We evaluate rGkCM on simulated trajectories with varying outlier levels and demonstrate significant computational speedup over the heuristic unweighted GkCM (uGkCM) method while maintaining comparable accuracy. Finally, we validate the approach on a WAM-V autonomous surface vessel equipped with an acoustic beacon and GNSS ground truth, showing effective outlier rejection in a shallow, multipath-prone marina. Results indicate that rGkCM enables robust and efficient outlier rejection for real-world bearing-based localization tasks.