中文摘要：

定位服务是普适计算所必须提供的基本服务之一．然而由于测量误差的存在，定位误差在所难免．首先围绕如何减小定位误差，提出并证明了误差收敛定理，揭示了不同位置的参考点对定位误差的贡献规律；其次针对普适计算的实际应用，提出了参考点选择的最佳计算单元和混沌三角形定位参考点选择算法．性能分析及仿真实验表明，所提出的定位参考点选择算法较传统的多边形定位算法在满足相同定位精度需求的情况下，所需的系统开销小、定位误差收敛速度快，更适合为资源受限环境下的普适计算定位服务所使用．

英文摘要：

Positioning service is one of the basic services required by practical application of ubiquitous computing and how to obtain location information of an unknown node precisely is a key problem of positioning service in ubiquitous computing. However, positioning error is inevitable due to various potential errors caused by imprecise measuring instruments, improper measuring methods, etc. Firstly, a new error convergence theorem is presented and proved about how to reduce positioning error rapidly. The theorem is composed of three sub-theorems which indicate respectively how to make the smallest initial positioning error, how to reduce the initial location error more quickly by topological replication of reference nodes, and how to converge the initial location error to obtain minimal location error. Secondly, with a view of the actual application in ubiquitous computing, the optimal computing unit of reference nodes selection is proposed and the location reference node selection algorithm is put forward using topological duplication according to chaos triangles based on the presented error convergence theorem. Performance analysis and simulation experiments indicate that the location reference node selection algorithm is more suitably applied in resource-constrained environment of ubiquitous computing with less system cost and faster positioning error convergence than the traditional polygonal positioning algorithm at the same location accuracy.