GNSS精密单点定位中的数学模型  

Mathematical Model of GNSS Precise Point Positioning

作　　者：黄云清[1] 梁琴[1] 唐启立 杨银[1] 张佳豪 HUANG Yunqing;LIANG Qin;TANG Qili;YANG Yin;ZHANG Jiahao(National Center for Applied Mathematics in Hunan,Xiangtan University,Xiangtan,Hunan 411105,China)

机构地区：[1]湘潭大学湖南国家应用数学中心,湖南湘潭411105

出　　处：《数学建模及其应用》2024年第4期1-10,共10页Mathematical Modeling and Its Applications

基　　金：国家重点研发计划(2020YFA0713500);湖南省教育厅重点项目(22A0126);湖南省科技厅科研基金项目(2023GK2029,2022JJ30555);湖南省普通高等学校科技创新团队支持项目(数学共性基础算法研究)。

摘　　要：GNSS精密单点定位(precise point positioning,PPP)技术是一类基于卫星信号,实现全球精密定位的方法,其工作原理为采用一台GNSS接收机的双频码和载波相位观测值,利用精密轨道和精密钟差产品,同时应用精细化的误差修正数学模型,进行单站绝对定位.PPP不依赖地面基准站,它的出现改变了以往只有载波相位双差观测模型才能达到高精度定位的情况,是GNSS定位技术中继RTK和网络RTK技术之后的又一次技术革命.本文主要介绍了PPP中的双频消电离层组合的定位方程组、误差修正数学模型以及参数估计的最小二乘方法,并通过算例展示了PPP的有效性.GNSS Precise Point Positioning(PPP)technology is a method based on satellite signals to achieve global precise positioning.Its working principle is to use the dual-frequency code and carrier phase observation of a GNSS receiver,and use precision orbit and precision clock products.At the same time,refined mathematical models of error correction are applied to position a single station.PPP does not depend on any reference station,and its appearance changes the situation that only the carrier phase double difference observation model can achieve high-precision positioning in the past.PPP is another technical revolution of GNSS positioning technology after RTK and network RTK technology.This paper introduces the positioning equations,which uses the combination of dual frequency to eliminate ionosphere,the mathematical models for error correction and the least squares method for solving the corresponding equations.We also demonstrate the effectiveness of this model through numerical examples.

关 键 词：精密单点定位 双频消电离层组合 误差模型 线性化 最小二乘方法 

分 类 号：P228.1[天文地球—大地测量学与测量工程]