基于整数最小二乘估计的广义模糊度解算理论与方法研究

With the rapid development of GPS, BDS and other global navigation satellite systems, it will provide more satellite observations to improve the precision, reliability and availability of satellite navigation and positioning services. However, as the increase of the number of satellite observation equations, it will inevitably bring about a hard problem to fast and reliably resolve high-dimensional ambiguity, which has become a bottleneck problem that affects the multi-GNSS integrated precise positioning. The purpose of this project is to solve the problems of high-effective blocking decorrelation of high-dimensional ambiguity, optimal construction of the selection criteria of partial ambiguity resolution subsets, fast ambiguity search under quadratic constraint of baseline. Then, a theoretical method of generalized ambiguity resolution is built perfectly based on the integer least-squares (ILS) estimation to solve the full and partial solution, the baseline constrained and unconstrained solution of ambiguity, so as to realize the fast and high-effective fixing of high-dimensional ambiguity and enhance the application effect of multi-frequency and multi-GNSS integrated precise positioning. This research is in line with the development trend of GNSS towards multi-GNSS and multi-frequency. And this research can enrich the theory and method of satellite navigation and positioning, and have important academic value and broad application prospects. This project will be carried out under mature conditions and expected to achieve innovative research results.

随着GPS、BDS等GNSS系统的快速发展，在提供更多的卫星观测信息来提高卫星导航定位服务的精度、可靠性和可用性的同时，也不可避免地带来了高维模糊度的快速可靠解算难题，其已成为影响GNSS多系统融合精密定位效果的瓶颈问题。本项目旨在解决基于整数最小二乘估计的高维模糊度的高效分块降相关、部分模糊度解算子集选取准则的最优构建、基线长二次型约束下模糊度快速搜索等关键问题，建立可以解算模糊度的整体解和部分解、基线约束解和非约束解的广义模糊度解算理论方法，实现高维模糊度的快速、高效固定，提升GNSS多频多系统融合精密定位的应用效果。项目研究符合当前GNSS朝多频多系统方向发展的趋势，丰富了卫星导航定位的理论和方法，具有重要的学术价值和广阔的应用前景。本项目研究条件基本成熟，有望取得创新性的研究成果。

本项目从整数最小二乘估计的角度对模糊度降相关、部分模糊度解算和附有基线长约束的模糊度解算等三个方面开展研究，解决模糊度降相关性能评估和快速估计、部分模糊度解算子集选取准则的最优构建、基线长二次型约束下模糊度快速搜索等关键问题，建立可以解算模糊度的整体解和部分解、基线约束解和非约束解的广义模糊度解算理论体系，实现模糊度的快速、高效固定，提升GNSS多频多系统融合精密定位的应用效果。.针对上述研究目标，本项目的主要研究内容如下：.(1) 在模糊度降相关方面，理论上推导了基于下三角Cholesky分解多维整数高斯变换的降相关条件，提出了LIGT算法，为基于下三角Cholesky分解的相关降相关算法性能进行合理性评估提供了对比算法；指出了降相关性能与条件方差数值序列的平稳性有关，降相关性能越强，条件方差数值序列越平稳，在此基础上定义了合理评定降相关性能的“条件方差平稳度”指标，完善了模糊度降相关理论体系。.(2) 在部分模糊度解算方面，理论上证明了两种求取基线固定解方式的等价性，为直接采用模糊度固定子集求解基线向量提供了理论依据；定义了基线增益函数作为判断模糊度子集固定与否的指标，有效顾及了模糊度部分固定对基线精度的影响；提出了基于基线增益函数的TC-PAR方法，该方法相对于LAMBDA算法能较大程度地提高模糊度的固定率。.(3) 在附有基线长约束的模糊度解算方面，详细评估了观测方程联解法、CLAMBDA法和判别条件法这三种基线长约束方法的性能差异；提出了基于缩放因子自适应调整搜索空间的ASS算法，并讨论了采用上下边界分别设置初始空间对ASS算法的影响。结果表明，ASS算法采用缩放因子可以有效地调整搜索空间，提高弱GNSS模型下CLAMBDA的搜索效率；基于下边界设置初始空间可以进一步提高ASS算法的解算性能，为后续CLAMBDA算法研究如何设置初始空间明确了方向。