一种伪距单点定位的数学模型研究及程序实现

A mathematical model of pseudo-range single point positioning and its programming

对伪距单点定位的数学模型进行了详细分析,列出详细步骤和误差方程式,包括中间涉及到的坐标转换以及一些重要技术细节,并通过编程实现计算测站点各历元单点定位的空间直角坐标XYZ以及综合各历元数据计算得到的坐标.利用若干工程实测获得的原始数据,并转换为RINEX格式,采用GPS卫星的伪距观测值和导航N文件计算得到测站点坐标,与接收机自带的程序计算的近似坐标进行坐标比较和精度分析,结果显示坐标较差在米级左右,而单点定位的精度为米级.证明该数学模型是可行的,且易于通过编程实现.

In this paper,the mathematical model of pseudo-range single-point positioning is analyzed in detail,and detailed steps and error equations are listed,including coordinate transformation and some important technical details involved.The spatial rectangular coordinates XYZ of single-point positioning of each epoch of the station and coordinates calculated by synthesizing metadata of each epoch are calculated by programming.Using the original data obtained from some engineering surveys and converted into RINEX format,the coordinates of the surveying station are calculated by using the pseudo-range observation value of GPS satellite and navigation N file.The coordinates are compared and analyzed with the approximate coordinates calculated by the program of the receiver.The results show that the coordinates are about meter-level,while the accuracy of single-point positioning is meter-level.It is proved that the mathematical model is feasible and easy to be realized by programming.