A Closed-Form Configuration Design Law for Dual-UAV Bearing-Only Localization of Moving Ground Targets Under Field-of-View Constraints

Empirical standoff and look-ahead selection motivates this closed-form law for passive dual-UAV bearing-only localization in a wall-type leader–follower formation. An off-axis-dependent bearing-noise model with a nonzero floor yields the Fisher information matrix, Cramér–Rao lower bound ellipse area, and A-optimal information trace. Under sufficient conditions for a symmetric configuration, both bounds increase strictly with standoff, so the field-of-view (FOV) lower bound sets the optimum rather than an interior stationary point. The FOV region also yields closed-form baseline and look-ahead limits. The law is Rp⋆≈min(Rmax,κsdFOV), where dFOV = l/(2tanφ) and κs = 1.5–2 is recommended for the investigated straight-cruise domain. Twenty-one 30-run straight-cruise Monte Carlo grids gave mean κs = 1.61 and unchanged values over tested noise and speed ranges; independent baseline and field-of-view combinations later show that κs is a domain-specific empirical coefficient rather than a universal constant. Using separate selection and test seeds, the frozen direct law reduced hard-turn overall mean position error (MPE) by 17.7% and 52.2% relative to dwell approximation and closed-loop rolling, respectively. Other scenarios precluded cross-scenario maneuver guarantees. The law provides preflight nominal placement; maneuvering requires dynamic feasibility, dropout, and estimator consistency checks before online adjustment.