A two-station over-the-horizon direction-finding localization method with tropospheric equivalent bearing-bias compensation

Abstract

Maritime over-the-horizon (OTH) two-station angle-of-arrival localization is affected by both Earth-curvature modeling errors and systematic bearing biases introduced by tropospheric scattering. To improve localization accuracy while retaining the existing two-station direction-finding architecture, this paper proposes a WGS-84-constrained weighted least-squares (WLS) method with tropospheric equivalent bearing-bias compensation. The method formulates the bearing geometry in the WGS-84 ellipsoidal reference frame and represents the angular deviation between the dominant scattered arrival direction and the true geometric bearing as a station-specific equivalent bias estimated from calibration data or prior information. Random direction-finding errors and residual compensation uncertainty are incorporated into the observation covariance matrix of the WGS-84-constrained WLS formulation. Monte Carlo simulations under a representative maritime OTH configuration show that the proposed method reduces the localization root-mean-square error (RMSE) from 50.71 km with conventional planar intersection and 11.07 km with uncompensated WGS-84-constrained WLS to 1.49 km. When the distance from the fixed station to the target varies from 400 km to 800 km, the RMSE remains below 2 km. With imperfect compensation, the RMSE remains approximately 4 km even when the standard deviation of the residual compensation error increases to 0.30∘. Tests on an independent validation dataset generated from realistic maritime scenario parameters yield an RMSE of 1.48 km, compared with 50.87 km and 11.85 km for the two baseline methods. These results demonstrate that the proposed method can jointly mitigate long-range curvature errors and tropospheric-scattering-induced bearing biases, offering a practical means of improving maritime OTH localization accuracy.