Kalman滤波估算电离层延迟的一种优化方法

频间偏差（Inter Frequency Bias，IFB）通常会给电离层延迟的解算带来误差.目前从电离层延迟中消除频间偏差的方法是基于GPS双频观测数据建立垂直电离层模型，利用卡尔曼滤波实时估算电离层模型系数和频间偏差.然而滤波过程中的测量噪声协方差矩阵没有考虑系统观测量之间的相关性，这会导致滤波模型不准确，进而影响最后求解的电离层延迟的准确性.本文选取了美国19个参考站的GPS双频观测数据，利用卡尔曼滤波实时估算电离层模型系数以及频间偏差.在滤波过程中，通过将先验频间偏差的估计方差引入测量噪声方差，实现对测量噪声协方差矩阵的优化.计算结果表明，优化后得到的卫星频间偏差与欧洲定轨中心（Center for Orbit Determination in Europe，CODE）得到的频间偏差更接近.将优化后的电离层延迟代入伪距解算，得到的位置误差的标准差在东向和天顶向分别下降了12.5%和15.4%，天顶向误差平均值下降了17.6%，定位精度得到提高. 

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.