相邻历元误差相关的抗差卡尔曼滤波算法分析

根据卡尔曼滤波理论以及抗差理论,本文推导出了相邻历元误差相关的抗差卡尔曼滤波模型,其对观测值中含有粗差有良好的抗差性。通过对含有粗差的变形监测数据分析,与相邻历元误差相关的卡尔曼滤波模型进行比较,采用本文构造的抗差卡尔曼滤波模型处理数据,无论是否有粗差存在观测值里,变形计算结果与实际结果大体一致,粗差对计算结果的影响不敏感。在对变形监测数据分析时,可得出卡尔曼滤波方法估计的状态向量,没有寄存大量的以往观测数据,而是使用最近的观测数据,经过不断的预测和改正,把新的状态展示在系统中。

The Analysis of Adjacent Epoch Error Related Robust Kalman Filtering Algorithm

According to the Kalman filtering theory and robust theory, we derived the model of adjacent epoch error related robust Kalman filtering algorithm. This model has a good robustness for observations containing gross errors. Through the analysis of deformation monitoring data containing gross errors and compare it to the model of adjacent epochs error related Kalman filtering algorithm, it can be concluded that using the proposed robust Kalman filtering model in data processing, regardless of whether or not there are gross errors in the observation values, the results of deformation analysis are consistent with the actual situation, which is not sensitive to the impact of gross error. And during the analysis of deformation monitoring data, we found that when the Kalman filtering method is used to estimate the state vector, it does not store a large amount of historical data, but takes use of the new observational data, through the continuous prediction and correction to estimate the new state of the system.