Hierarchical Bearing-only Multi-target Localization via Coarse-to-fine Grid Search and Nonlinear Refinement

The accurate localization of multiple targets is essential in sensing and surveillance applications. However, it is difficult to achieve when direct-range measurements are unavailable. In such cases, estimation relies solely on directional observations from multiple sensors, and performance often degrades due to overlapping measurements, ambiguous associations and incomplete data. This paper presents a bearing-only multi-target localization algorithm. This method applies a hierarchical coarse-to-fine grid search and residual-based nonlinear optimization. First, a coarse spatial score map is constructed in which each grid point receives a Gaussian-based similarity score between measured and predicted bearings. This step identifies candidate regions, which are subsequently on a finer grid. A sensor coverage mask is then used to ensure sufficient and independent measurement support. Finally, least-squares regression is applied to improve the estimates. The simulation results show that the proposed method preserves accuracy in the presence of measurement noise and partial observation loss. Therefore, the proposed method provides a practical solution for bearing-only multi-target localization in diverse sensing environments.