Abstract: 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 foundational 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 ex-press 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 higher-order error terms, which lead to 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, enhancing the accuracy of initial positioning. To further eliminate the impact of measurement errors on positioning performance, 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 involving 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) anal-ysis of the average results for far/near-range SOP positioning errors, Ts-GBr improves positioning performance by ap-proximately 50% compared to Ts-WLS.

Key words: The navigation and positioning based on SOP, integrate TDOA/AOA, bias-suppression, CRB