基于卡方检验的抗差自适应Kalman滤波在变形监测中的应用

摘要

Gross error cannot be avoided as observations will be affected by environmental and some uncertain factors.In this paper,we introduce two adaptive factors based on a robust Kalman filter to adjust imprecise dynamic models and observation models which interfuse gross error.According to the low efficiency of the robust adaptive Kalman filter,we construct achi-squared distribution based on a robust Kalman filter.We test gross error by chi-squared distribution,then use a robust adaptive Kalman filter to process data in these algorithms.Experimental results show that the algorithm of dual adaptive factors filtering can resist gross error efficiently and weaken adverse effects due to the imprecise dynamic model.A robust Kalman filter based on chi-squared distribution can resist the effects of gross error and the convergence rate will also be improved.%在抗差Kalman滤波的基础上引入双自适应因子,分别对动态模型不准确和观测模型存在粗差进行调节,构建双自适应因子滤波模型.针对抗差自适应Kalman滤波效率较低的缺点,通过构建基于卡方检验的抗差自适应Kalman滤波,先用卡方检验对粗差进行检验,再调用抗差自适应Kalman滤波进行处理.工程实例表明,双自适应因子滤波模型可以很好地抵御粗差,并减弱模型不精确的影响.基于卡方检验的抗差自适应Kalman滤波不仅可以削弱粗差对滤波估值的影响,而且可以提高数据处理的效率.