精密单点定位不等精度观测值的RKF研究

推导了精密单点定位含有粗差观测数据的M-LS滤波原理，对等价权阵采用三段降权函数实现抗差。从新息和残差的协方差关系出发，利用对粗差敏感的残差标准差作为抗差因子。通过迭代减弱卫星间载波残差及其抗差因子的相关性。针对载波和伪距观测值不等观测精度和不相关性，采用双抗差因子实现静态抗差卡尔曼滤波（robust Kalman filtering，RKF）。采用标准卡尔曼滤波、基于新息RKF、基于残差的增益矩阵双抗差因子RKF、基于残差的等价权阵双抗差因子RKF等4种模型，分别对一组实测数据解算分析。结果表明，基于新息RKF对精度较高的载波粗差不敏感；基于残差的增益矩阵RKF对载波较小的粗差抗差效果较差，且发生粗差历元时刻的状态参数与真值偏差较大；而基于残差构造的等价权阵双抗差因子RKF可以非常精确和高效地实现抗差，单个卫星粗差对测站位置参数影响小于1 mm。

Research on Robust Kalman Filter of Observations with Unequal Precision in Precise Point Positioning

The robust Kalman filter principle of precise point positioning is deduced. The standard deviation of residuals is used to construct robust factor based on IGGⅢ function by equivalent weight matrix, which is very sensitive to the outliers, because the residual covariance is smaller than the innovation covariance. The correlation of residuals and robust factor of carrier phase among satellites is greatly weakened by iterating. The robust factor of carrier phase and code are independently calculated, because of the unequal accuracy and irrelevant between carrier phase and code observations. Four models are used to test and analyze by the GPS dual-frequency observations, which included the standard Kalman filter, the robust Kalman filter (RKF) based on innovation, the RKF based on robust residuals and gain matrix, and the RKF based on robust residuals and equivalent weight matrix. Results show that it is insensitive to the outliers of accurate carrier phase observations, which the RKF based on innovation. The smaller carrier phase outliers are difficult to be detected via the RKF based on robust residuals and equivalent weight matrix, and the estimated coordinates has a large deviation from the true value in the epoch of outliers occurred. The RKF based on robust residuals and equivalent weight matrix can efficiently and accurately resist outliers, and the deviations between the estimated coordinates and true value is 1 mm smaller for the outliers of single satellite.