Robust SOP positioning algorithm based on tightly coupled TDOA/AOA

The navigation and positioning system based on Signals of Opportunity （SOP） serves as an effective supplement when the Global Navigation Satellite System （GNSS） is unavailable. Accurate SOP positioning is founda⁃ tional to achieving high-precision navigation. To this end， this paper proposes a robust positioning algorithm， namely the Two-step Geometrical Bias-restrain （Ts-GBr）， which integrates Time Difference of Arrival （TDOA） and Angle of Arrival （AOA）. Firstly， we linearly express the nonlinear positioning equations using a tightly coupled method， thereby mitigating the influence of initial values on convergence in traditional nonlinear positioning algorithms. Secondly， given that the Two-step Weighted Least Squares （Ts-WLS） method approximates weighting matrices and overlooks higherorder error terms， resulting in poor robustness and threshold effects， this paper proposes a more robust algorithm Ts- GBr. Ts-GBr constructs weighting matrices by evaluating positioning errors from heterogeneous measurements， en⁃ hancing the accuracy of initial positioning. To further eliminate the impact of measurement errors on positioning perfor⁃ mance， Ts-GBr recalculates the covariance matrix of positioning errors in the second step and establishes constraints for the tightly coupled positioning model. Theoretical analysis proves that Ts-GBr is an unbiased estimation algorithm and can approximate the Cramer Rao Bound （CRB）. Finally， the performance of Ts-GBr is tested under conditions in⁃ volving different measurement errors， receiver motion trajectories， and far/near-range SOP scenarios. Results indicate that Ts-GBr exhibits greater robustness. Based on the Root Mean Square Error （RMSE） analysis of the average re⁃ sults for far/near-range SOP positioning errors， Ts-GBr improves positioning performance by approximately 50% com⁃ pared to Ts-WLS.