多基准站相对定位算法及先验基线向量偏差影响分析

为提高单基准站短基线相对定位解算的可靠性，研究了多基准站约束的相对定位算法。将基准站间可提前测量的先验基线信息融入观测模型中，给出了多基准站相对定位的函数模型和随机模型，在此基础上推导了模糊度精度因子的解析表达式，揭示了基准站数量的增加对模糊度浮点解精度提升的作用；从理论上分析了基准站间先验基线信息中的偏差对模糊度解算的影响，分析表明，当先验基线各分量偏差的绝对值之和小于5 cm时，模糊度解算几乎不受影响；通过仿真和实测数据进行了验证。试验结果表明，增加基准站数量不仅能有效提升模糊度解算成功率和收敛速度，并且对先验基线信息中的偏差具有较好的抑制作用，当基线各分量偏差均增加到4 cm时，实测数据模糊度解算成功率仍能达到92%以上。研究结论为特殊场景下多基准站间的快速非精确标定提供了理论依据。

Multi-reference-station based relative positioning method and impact analysis of the biases in priori baseline vectors

In order to improve the reliability of the single-reference-station based relative positioning solutions over short baselines, the multi-reference-station based relative positioning method was explored. A priori baseline information between the reference stations was integrated into the observable model, thus giving the functional and stochastic models of the multi-reference-station based relative positioning. Based on that, the closed-form formula of the ambiguity dilution of precision for the positioning was derived so that the influence of the number of reference stations on the float ambiguity precision was revealed. Then the impacts of the biases in the a priori baseline information on the integer ambiguity resolution were analyzed theoretically. It show that the integer ambiguity resolution could barely be influenced on the condition that the bias is less than 5 cm. The multi-reference-station based relative positioning method was validated with both the simulated and real data sets. The numerical results show that, increasing the number of reference stations not only improves the single-frequency ambiguity resolution success rate and convergence rate, but also restrains the biases in the a priori baseline information. For example, the ambiguity resolution success rate is still larger than 92% even when the biases of the baseline components attain 4 cm in the field tests. This contribution provides the theoretical foundation for the fast and imprecise calibration between the multiple-reference-station in special scenarios.