Robust Helmert Variance Component Estimation for Positioning with Dual-Constellation LEO Satellites’ Signals of Opportunity

Abstract

In Global Navigation Satellite System (GNSS)-denied environments, navigation using signals of opportunity (SOP) from Low Earth Orbit (LEO) satellites is considered a feasible alternative. Compared with single-constellation systems, multiple-constellation LEO systems offer improved satellite visibility and geometric diversity, which enhances positioning continuity and accuracy. To allocate weights among heterogeneous observations, prior studies have employed the Helmert variance component estimation (HVCE) method, which iteratively determines relative weight ratios of different observation types through posterior variance estimation. HVCE enables error modeling and weight adjustment without prior noise information but is highly sensitive to outliers, making it vulnerable to their impact. This study proposes a Robust HVCE-based dual-constellation weighted positioning method. The approach integrates prior weighting based on satellite elevation, observation screening based on characteristic slopes, HVCE, and IGG-III robust estimation to achieve dynamic weight adjustment and suppress outliers. Experimental results over a 33.9 km baseline demonstrate that the proposed method attains Two-Dimensional (2D) and Three-Dimensional (3D) positioning accuracies of 12.824 m and 23.230 m, corresponding to improvements of 29% and 16% over conventional HVCE weighting, respectively. It also outperforms single-constellation positioning and equal-weighted fusion, confirming the effectiveness of the proposed approach.