不确定性数学理论在GNSS精确定位中的研究

【作者】 康荣雷；

【导师】 舒兰；

【作者基本信息】 电子科技大学 ， 运筹学与控制论， 2009， 硕士

【摘要】 卫星导航定位技术的发展,在各应用领域产生了巨大的经济与社会效益。通过捕获伪码计算伪距的传统定位模式,如今已经不能满足高精度定位的需求。载波相位定位技术的发展,一定程度上解决了这个问题,但双差定位模型需要实时获得基准站的差分信息,极大限制了载波相位定位技术的应用范围。本文以载波相位绝对定位模型为基础,探讨了整周模糊度解算与周跳检测修复的问题,将不确定性数学理论融入其中,进行了开创性的研究。本文首先介绍了传统伪距定位模型,并通过简化矩阵的特性,利用QR分解,提出了新的递推解算算法。然后研究了载波相位测量与定位的原理,并建立了静态与动态的绝对定位模型。分析出载波相位精确定位的难点,集中在整周模糊度求解和周跳检测与修复方面。在整周模糊度的解算中,首先总结传统解算算法,分析传统方法的不足,由于解算矩阵的病态性严重,导致模糊度搜索集合的区域极大。本文结合不确定性数学中的粗糙集理论,提出粗糙规整映射,设计了变粒度搜索算法,简化了搜索区域的结构,可实现整周模糊度解组合的快速搜索,并结合RATIO检验,快速得到正确解。仿真结果表明,该算法较传统方法可有效提高整周模糊度的解算效率。周跳检测与修复,作为载波相位定位所用原始数据的预处理步骤,是完好性检测的重要部分。本文首先分析了通过研究载波观测值序列的数学特性,利用时间序列分析的方法,结合数据之间的相关性信息,提出基于模糊数学理论的数据相关度概念,通过对所建AR ( p )模型的分析,得出当3≤p≤5时是折中性选择,利用数据相关度对三组模型进行了加权组合,仿真结果表明,该算法较传统方法更能有效的检测与修复周跳。更多还原

【Abstract】 With the development of GNSS, huge benefit has been produced. The traditional orientation pattern is unable to satisfy the requirement of the high precision orientation. Carrier phase measurement solves the problem in a certain extent. This paper makes researches on ambiguity estimation and circle slips detection based on the carrier phase measurement model using the uncertainty mathematics theory to solve those problems.At first, the traditional orientation model using pseudorange is introduced. With the characteristics of the predigesting matrix and QR analysis, a new algorithm has been found, so we create the static and dynamic models for the absolute orientation. The conclusion indicates that the difficulties are ambiguity estimation and circle slips.In the study of ambiguity estimation, we firstly make a summary of the traditional algorithms and analyze those deficiencies. The oversize condition-number of the matrix brings on the oversize searching area for the ambiguity. With the rough sets theory in uncertainty mathematics, the original theory named Rough Integer Mapping is brought forward to solve those problems. Searching algorithm with granularity changing is designed and predigests the topology of the ambiguity searching area. With RATIO test, the right ambiguity combinations could be confirmed quickly. The simulation indicates that the new algorithm could enhance the efficiency of ambiguity estimation obviously.As the pretreatment of the original data for the carrier phase orientation, the detection and adjustment of the circle slips, is important department of the RAIM. The mathematic characteristics of the carrier phase observation serials are analyzed firstly. Using Time Serial Analysis method and the pertinency information between the neighbor data, we get the conception of data correlation based on Fuzzy mathematics theory. Through analyzing the AR ( p )model, we get the range:3≤p≤5, and combine the three models using the data correlation theory. The simulation indicates that this new algorithm can get an effective result for detection and adjustment of cycle slips.更多还原