GNSS速度测量若干数学模型研究

Research on some mathematical models of GNSS velocity determination

为解决GNSS伪距变率双差测速和高斯投影、墨卡托投影坐标系中的速度投影计算问题,以大地坐标速度为未知数,推导GNSS伪距变率双差测速解法,基于高斯投影、墨卡托投影公式,推导其速度投影算法。建立了以大地坐标速度为未知数的GNSS伪距变率双差测速数学模型,建立了高斯投影、墨卡托投影坐标系速度投影计算方法,给出了应用试验和算例。结果表明,GNSS伪距变率双差测速大地坐标分量精度达到毫米/秒级,高斯投影、墨卡托投影坐标系速度投影算法正确。提出的GNSS伪距变率双差测速解法具有重要的应用价值。提出的高斯投影、墨卡托投影坐标系速度投影数学模型,可以满足低、中、高速应用需要。

In order to solve the problem of velocity determination of the GNSS pseudo-range rate double difference,taking the geodetic coordinate velocity as unknow n,the solution method of velocity determination of the GNSS pseudo range rate double difference is derived,and based on the Gaussian projection and Mercator projection formulas,velocity projection algorithms are obtained.In this paper,the mathematical model w ith geodetic coordinates velocity as unknow n of velocity determination of the GNSS pseudo-range rate double-difference is established,the application tests and calculation examples are given.The results of experiments and numerical examples show that the accuracy of the geodetic coordinate velocity component of GNSS pseudo-range rate double difference reaches mm/s level,and the velocity projection algorithm of Gaussian coordinate system and Mercator coordinate system are correct.The proposed velocity determination method of GNSS pseudo-range rate double difference in this paper has important application value.The proposed mathematical model of speed projection of Gaussian projection and Mercator projection coordinate system can meet the needs of low medium and high speed applications.