空间球交会的三维加权质心室内定位算法

Three-dimensional weighted centroid indoor positioning algorithm based on sphere intersection

针对室内定位缺少全球导航卫星系统(GNSS)信号,且传统定位方式定位精度特别是在高程上精度较低的问题,在分析普通三维定位算法、基于场强的三维加权定位算法和基于距离的三维加权定位算法基础上,提出了一种空间球交会的三维加权质心室内定位算法.该方法以未知点与接入点之间距离为半径绘制空间球体,任意两个空间球体构成一个空间球体对,将空间球体对位置关系划分为5种情况;引入前方交会原理,推导空间球体对与待测未知点的几何关系,反演得出5种情况的坐标计算公式;将距离倒数作为参考点权因子,计算未知点三维加权坐标.实验表明:该方法比普通三维定位算法、基于场强的三维加权定位算法和基于距离的三维加权定位算法定位误差明显减小,在点位高程方向上比这3种方法定位精度提高40%以上.

Aiming at the problems of lacking global navigation satellite system （GNSS） signals and low positioning accuracy especially for elevation in the traditional indoor positioning methods, a three-dimensional weighted centroid indoor location algorithm based on sphere intersection was proposed in this paper by studying and analyzing the three common algorithms, i. e. ordinary three-dimensional positioning algorithm, three-dimensional weighted localization algorithm based on field intensity, and three-dimensional weighted localization algorithm based on distance. Firstly, a spacial sphere was drawn by taking the distance between the unknown point and the access point as the radius, forming sphere pairs. Then it could be divided into five cases of the positional relationships. According to the principle of forward intersection, the geometrical relationships between unknown points and spheres were deduced, and the coordinates formulas of the five cases were obtained. Then the final three-dimensional weighted coor- dinates of the unknown points were computed by taking the inverse of distance as the weighting factor of the reference point. Experimental results show that the mean errors by this method are significantly reduced comparing with the ordinary three-dimensional positioning algorithm, three-dimensional weighted localization algorithm based on field intensity, and three-dimensional weighted localization algorithm based on distance, and especially the positioning accuracy in the vertical elevation could be improved by 40＆ or more than the common three methods.