Robust trajectory triangulation for UAV visual localization via iteratively reweighted least squares

Accurate localization of ground targets using monocular vision from a fixed-wing unmanned aerial vehicle (UAV) in tracking mode is a challenging problem in computer vision and photogrammetry. Classical triangulation methods often suffer from rank deficiency due to degenerate observation geometry. The trajectory triangulation paradigm overcomes this limitation by parameterizing target motion, yet existing solvers typically assume Gaussian-distributed observation noise with uniform weights, making them vulnerable to non-uniform noise induced by the UAV's high-speed maneuvering and to image matching outliers. This paper proposes a robust trajectory triangulation algorithm based on iteratively reweighted least squares. The proposed method constructs a target motion model tailored to the fixed-wing UAV's viewing geometry and incorporates robust M-estimation kernel functions, transforming the optimization into a sequence of adaptively weighted subproblems. The algorithm dynamically adjusts the weight of each observation ray according to its residual magnitude, effectively suppressing outlier interference while preserving computational efficiency. Experiments on numerical simulation and Gazebo simulation demonstrate that the proposed method outperforms baseline linear solvers and nonlinear least-squares optimizers in localization accuracy, especially in challenging circling tracking scenarios characterized by high dynamics and noise, reducing the mean localization RMSE by 75.8% and 68.3% compared with the baseline linear solver and the nonlinear least-squares optimizer, respectively.