自动确定边角混合网独立闭合差的增量算法

Incremental Algorithm for Automatically Determining Independent Misclosures in Hybrid Triangulation Networks

为评定外业观测数据质量和发现粗差,提出了一种闭合差搜索的通用算法。首先,针对高速铁路隧道中的各类边角混合网,基于平差理论,计算由边角混合网中测站数、非测站数和观测数确定其独立闭合差的数目,给出最简闭合差构成原则,求出余弦和正弦闭合差,推导闭合差限差计算模型,建立由闭合差探测观测值粗差的方法;进而导出闭合差增量与测站递增产生的重叠观测点数之间的数学关系式,设计数据结构实现测站与结点间双向多对多的拓扑映射关系,并基于分治思想,提出队列-测站双循环的增量算法来自动搜索最简且独立的闭合差;最后,以西南某高速铁路隧道构建的边角混合网为例进行算法验证。结果表明:增量算法能够在混合网中自动确定100%数量的最简独立闭合差,对观测值中存在的粗差100%予以探测,验证了采用该算法搜索闭合差及检核粗差的有效性。

To assess the quality of field observation data and detect gross errors,a generalized algorithm for searching misclosures is proposed.First,based on adjustment theory,the number of independent misclosures in all sorts of triangulations for high-speed railway tunnels is determined,considering the numbers of survey stations,non-station points and observations.The principle for constituting the simplest misclosure is established,based on which the cosine and sine misclosures are proposed.A computation model for the misclosure tolerance is derived,and a method for detecting gross errors in observations using misclosures is established.Next,the mathematical relationship is derived between the misclosure increment and the number of overlapping observation points resulting from a station increment.The bi-directional many-to-many topological relations are established between stations and nodes using a data structure,and based on a divide-and-conquer approach,an increment algorithm with dual loops for queue-station relations is proposed to automatically search for the simplest and independent misclosures.Finally,the algorithm is tested by an example of hybrid triangulation network constructed in a high-speed railway tunnel in southwest China.The results indicate that the incremental algorithm can automatically determine 100%of the simplest independent misclosures and detect 100%of the gross errors existed in observations,which validates the effectiveness in searching for misclosures and detecting gross errors by the proposed algorithm.