Optimization of Kalman Filtering in Estimating Ionospheric Delay

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.