Volume 41 Issue 2
Mar.  2021
Turn off MathJax
Article Contents
XUE Weifeng, NI Yude. Optimization of Kalman Filtering in Estimating Ionospheric Delay[J]. Chinese Journal of Space Science, 2021, 41(2): 273-278. doi: 10.11728/cjss2021.02.273
Citation: XUE Weifeng, NI Yude. Optimization of Kalman Filtering in Estimating Ionospheric Delay[J]. Chinese Journal of Space Science, 2021, 41(2): 273-278. doi: 10.11728/cjss2021.02.273

Optimization of Kalman Filtering in Estimating Ionospheric Delay

doi: 10.11728/cjss2021.02.273
  • Received Date: 2019-08-19
  • Rev Recd Date: 2020-05-05
  • Publish Date: 2021-03-15
  • IFB (Inter-Frequency Bias) is the difference between the hardware delays of two frequencies in the GPS (Global Positioning System) satellite transmitter and the user receiver. It is also called the Instrumental Bias, which will introduce errors into the solution of the ionospheric delay. The current method of eliminating the IFB from the ionospheric delay is to establish a vertical ionospheric model based on GPS dual-frequency observation data and estimate the ionospheric model coefficients and IFBs in real time using Kalman filtering. However, the measurement noise covariance matrix in the filtering process does not consider the correlation between the system observations, which leads to inaccurate filtering models. Finally, it will affect the accuracy of the solved ionospheric delay. In this paper, the GPS dual-frequency observation data of 19 reference stations in the United States are selected, and the ionospheric model coefficients and the IFBs are estimated in real time by Kalman filter. In the filtering process, the estimation noise variance matrix is optimized by introducing the estimated variance of a priori IFB into the measurement noise variance. The calculation results show that the IFBs of satellites after optimization is closer to the related IFB of CODE (the Center for Orbit Determination in Europe). Substituting ionospheric delay after optimization into pseudo-range resolution, the standard deviation of the position error obtained by substituting the pseudo-range solution decreases by 12.5% and 15.4% respectively in the eastward direction and the zenith direction. The average error in the zenith direction decreased by 17.6%, thus the positioning accuracy was improved.


  • loading
  • [1]
    WANG N, YUAN Y, LI Z, et al. Determination of differential code biases with multi-GNSS observations[J]. J. Geodesy., 2016, 90(3):209-228
    ARIKAN F, NAYIR H, SEZEN U, et al. Estimation of single station interfrequency receiver bias using GPS-TEC[J]. Radio Sci., 2008, 43(4):1-13
    YUAN Yunbin, OU Jikun. The influence of instrument deviation in GPS observation data on determining ionospheric delay and processing method[J]. Acta Geod. Cartograph. Sin., 1999, 28(2):110-114 (袁运斌, 欧吉坤. GPS观测数据中的仪器偏差对确定电离层延迟的影响及处理方 法[J]. 测绘学报, 1999, 28(2):110-114)
    MANUEL Hernández-Pajares, JUAN J M, SANZ J, et al. The ionosphere:effects, GPS modeling and the benefits for space geodetic techniques[J]. J. Geodesy., 2011, 85(12):887-907
    WANG Xiaolan, MA Guanyi. Ionospheric TEC and hardware delay inversion method based on dual-frequency GPS observation[J]. Chin. J. Space Sci., 2014, 34(2):168-179 (王晓岚, 马冠一. 基于双频GPS 观测的电离层TEC与硬件延迟反演方法[J]. 空间科学学报, 2014, 34(2):168-179)
    CHANG Qing, ZHANG Donghe, XIAO Zuo, et al. Hardware delay estimation method for GPS system and its application in TEC calculation[J]. Chin. J. Geophys., 2001, 44(5):596-601 (常青, 张东和, 萧佐, 等. GPS系统硬件延迟估计方法及其在TEC计算中的应用[J]. 地球物理学报, 2001, 44(5):596-601)
    LANYI G E, ROTH T. A comparison of mapped and measured total ionospheric electron content using global positioning system and beacon satellite observations[J]. Radio Sci., 1988, 23(4):483-492
    SARDÓN E, RIUS A, ZARRAOA N. Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations[J]. Radio Sci., 1994, 29(3):577-586
    SCHAER S. Mapping and Predicting the Earths Ionosphere Using the Global Positioning System[D]. Bern:University of Bern, 1999
    LI Z, YUAN Y, FAN L, et al. Determination of the differential code bias for current BDS satellites[J]. IEEE Trans. Geosci. Remote Sens., 2014, 52(7):3968-3979
    LEE H K, RIZOS C. Position-domain hatch filter for kinematic differential GPS/GNSS[J]. IEEE Trans. Aerosp. Electron. Syst., 2004, 44(1):30-40
    YICHUNG C. Real Time Implementation of the Wide Area Augmentation System for the Global Positioning System with an Emphasis on Ionospheric Modeling[D]. Stanford:Stanford University, 1997
    GENG Changjiang, ZHANG Hongping, ZHAI Chuanrun. Real time estimation of dcb using Kalman filters[J]. Geomat. Inf. Sci. Wuhan Univ., 2009, 34(11):1309-1311 (耿长江, 章红平, 翟传润. 应用Kalman 滤波实时求解硬件延迟[J]. 武汉大学学报:信息科学版, 2009, 34(11):1309-1311)
    ANDRÉ Hauschild, MONTENBRUCK O. A study on the dependency of GNSS pseudorange biases on correlator spacing[J]. GPS Solut., 2016, 20(2):159-171
    CHUI C K, CHEN G. Kalman filtering with real time applications[J]. Appl. Opt., 1989, 28:1841
    ZHANG Hongping. Research on Regional Ionospheric Monitoring and Delay Correction Based on Ground-based GPS[D]. Shanghai:Graduate School of Chinese Academy of Sciences, 2006 (章红平. 基于地基GPS的中国区域电离层监测与延迟改正研究[D]. 上海:中国 科学院研究生院, 2006)
    BLANCH J, WALTER T, ENGE P. Ionospheric threat model methodology for WAAS[J]. Navigation, 2002, 49(2):103-107
    SIMON D. Kalman filtering with state constraints:a survey of linear and nonlinear algorithms[J]. IET Control Theory Appl., 2010, 4(8):1303-1318
    SIMON D, CHIA T L. Kalman filtering with state equality constraints[J]. IEEE Trans. Aerosp. Electron. Syst., 2002, 38(1):128-136
    ZHANG Baocheng, OU Jikun, YUAN Yunbin, et al. Precise single point localization algorithm based on GPS dual-frequency original observation and its application[J]. Acta Geod. Cartograph. Sin., 2010, 39(5):478-483 (张宝成, 欧吉坤, 袁运斌, 等. 基于GPS双频原 始观测值的精密单点定位算法及应用[J]. 测绘学报, 2010, 39(5):478-483)
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article Views(346) PDF Downloads(50) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint