基于机会信号(Signals of Opportunity, SOP)的导航定位是卫星导航定位系统(Global Navigation Satellite System, GNSS)应用条件受限时的有效补充,准确的SOP位置信息是实现高精度SOP导航定位的前提。为此,本文提出了一种联合到达时差(Time Difference of Arrival, TDOA)和到达角(Angle of Arrival, AOA)的SOP鲁棒定位算法(Two-step Geometrical Bias-restrain, Ts-GBr)。首先,通过紧耦合TDOA和AOA线性化定位方程,避免了迭代初值对传统非线性定位算法收敛性的影响。其次,针对常用于求解紧耦合模型的两步加权法(Two-step Weighted Least Squares, Ts-WLS)近似了加权矩阵并忽略了误差的高阶项,导致异质观测量的加权方式鲁棒性低且算法易具有门限效应的问题,本文提出了鲁棒的Ts-GBr定位算法。该算法通过评估不同时刻异质观测量引起的定位误差来构建权值矩阵,提升鲁棒性;通过计算紧耦合定位模型的扰动误差来构建约束条件抑制偏差,进一步提升定位精度。通过理论分析Ts-GBr的无偏性及估计误差下界,证明该算法能逼近克拉美罗界(Cramer Rao bound, CRB)。最后,在不同测量误差、接收机运动轨迹、及对远/近距离SOP定位的情况下对Ts-GBr的性能进行了测试,结果表明Ts-GBr更具鲁棒性。平均算法对远/近SOP定位误差的均方根误差(Root Mean Square Error, RMSE)结果可知,Ts-GBr相较于Ts-WLS能够提升约50%的定位性能。
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.