A Method for Estimating Ionospheric Power Spectral Density in BDS Undifferenced and Uncombined PPP

XU Zongqiu; ZHANG Hongyang; XU Yantian; LI Jun; YANG Nannan; SHI Shuai

doi:10.13203/j.whugis20220752

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A Method for Estimating Ionospheric Power Spectral Density in BDS Undifferenced and Uncombined PPP

Geodesy and Survey Engineering | 更新时间：2026-11-05

- A Method for Estimating Ionospheric Power Spectral Density in BDS Undifferenced and Uncombined PPP
- Geomatics and Information Science of Wuhan University Vol. 50, Issue 4, Pages: 628-636(2025)
- 作者机构：
  
  1.辽宁工程技术大学测绘与地理科学学院，辽宁阜新，123000
  2.中国测绘科学研究院，北京，100036
  3.中国建筑一局（集团）有限公司，北京，100161
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(42074012;42030109);Liaoning Key Research and Development Program(2020JH2/10100044)
- DOI：10.13203/j.whugis20220752
  CLC： P228
- Received：06 February 2023，
  
  Published：05 April 2025
- 稿件说明：
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徐宗秋,张鸿洋,徐彦田，等.一种BDS非差非组合PPP中电离层功率谱密度估计方法[J].武汉大学学报（信息科学版）,2025,50(4):628-636.

XU Zongqiu,ZHANG Hongyang,XU Yantian,et al.A Method for Estimating Ionospheric Power Spectral Density in BDS Undifferenced and Uncombined PPP[J].Geomatics and Information Science of Wuhan University,2025,50(4):628-636.
徐宗秋,张鸿洋,徐彦田，等.一种BDS非差非组合PPP中电离层功率谱密度估计方法[J].武汉大学学报（信息科学版）,2025,50(4):628-636. DOI：,10.13203/j.whugis20220752

XU Zongqiu,ZHANG Hongyang,XU Yantian,et al.A Method for Estimating Ionospheric Power Spectral Density in BDS Undifferenced and Uncombined PPP[J].Geomatics and Information Science of Wuhan University,2025,50(4):628-636. DOI：,10.13203/j.whugis20220752

摘要

无电离层组合模型和非差非组合模型是精密单点定位(precise point positioning，PPP)中最常用的两种函数模型。非差非组合模型中电离层误差常被描述为随机游走，随机游走过程中的功率谱密度成为决定PPP定位性能的主要因素，采用经验值功率谱密度的方法没有考虑电离层小尺度变化。在非差非组合模型的基础上，分析电离层时间相关性信息，在电离层差分时间间隔较小时，观测噪声较大甚至淹没电离层的变化。因此，通过平滑去噪的方法削弱观测值噪声的影响，实时确定电离层功率谱密度，对非差非组合模型中的电离层延迟参数进行合理约束，从而改善定位性能。对12个测站10 d的北斗卫星导航系统(BeiDou satellite navigation system，BDS)数据进行不同电离层模型下的解算，结果表明：相对于传统无电离层组合PPP模型，所提方法在收敛时间上缩短约8.2%，水平方向精度相当，垂直方向定位精度提高约31%。相较于功率谱密度采用经验值方法，所提方法在收敛时间上缩短约9.7%，水平方向精度相当，垂直方向定位精度提高约31%。

Abstract

Objectives

The ionosphere-free (IF) model and the undifferenced and uncombined (UDUC) model are the two most commonly used functional models in precise point positioning (PPP). In the UDUC model

the ionospheric error is often described as random walk parameter

and the power spectral density (PSD) in the process of random walk becomes the main factor determining the positioning performance of PPP. The method of determining the PSD by the empirical value can not show the small scale variation of the ionosphere.

Methods

Based on the UDUC model

the time correlation information of the ionosphere is analyzed. When the difference time interval of the ionosphere is small

the observation noise is large and it will submerge the changes of the ionosphere.Hence

we use the smooth denoising method to weaken the influence of the observation noise

determine the ionospheric PSD in real time

and reasonably constrain the ionospheric delay parameters in the UDUC model

so as to improve the positioning performance.

Results

The experiment was carried out through 10 d BeiDou satellite navigation system (BDS) observations come from 12 stations under different ionospheric models. The results show that compared with the traditional ionospheric-free model

the convergence time of the proposed method is shortened by 8.2%

the horizontal direction accuracy is equivalent

and the vertical direction positioning accuracy is improved by about 31%. Compared with the empirical value PSD method

the convergence time of the proposed method is shortened by about 9.7%

the horizontal direction accuracy is equivalent

and the vertical direction positioning accuracy is improved by about 31%.

Conclusions

We recommend that BDS users adopt our proposed method when using UDUC model

which can effectively shorten the convergence time and improve the positioning accuracy to a certain extent.

关键词

Keywords

references

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