数据同化系统中的集合时间局地化鲁棒滤波方法

摘要

针对传统的卡尔曼滤波方法对不确定因素不具备鲁棒性问题,在集合鲁棒滤波的基础上,提出一种从观测角度构建优化数据同化的方法,称之为放大观测协方差矩阵的集合时间局地化鲁棒滤波,并推导了新方法的算法准则和递归公式.利用非线性系统Lorenz-96模型,基于性能水平系数、驱动参数、观测数目和集合数目变化的条件,对新方法和集合卡尔曼滤波方法的鲁棒性和同化精度进行比较.结果表明:集合卡尔曼滤波方法的均方根误差大于时间局地化鲁棒滤波的;在观测数或集合数较少的情况下,集合卡尔曼滤波出现了滤波发散问题,而鲁棒滤波的均方根误差波动较小;相较于传统的集合卡尔曼滤波算法,观测角度构建的时间局地化的H∞滤波方法对系统参数的变化更具鲁棒性,滤波精度更高.%The traditional Kalman filter algorithm is not robust with uncertain parameters.In view of this and based on the ensemble robust filters, the optimal method of data assimilation constructed from observations, which was referred to as the ensemble time-local robust filter of inflating the observational covariance matrices, was presented, and the rule of the algorithm and the inference of the formula of the approach presented were given.The approach presented was compared with the ensemble Kalman filter method on the robustness and the assimilation accuracy using the strongly nonlinear Lorenz-96 model and on the basis of the changeable condition of the performance level parameters,the force parameters, and the size of observations and ensemble.The results suggest that:the root mean square errors of the ensemble Kalman filter method are much larger than those of the time-local robust filter;the ensemble Kalman filter produces filter divergence with a relatively small observation or ensemble size, while the root mean square error of the robust filter has slightly change; compared with the traditional ensemble Kalman filter algorithm, the time-local H∞filter approaches using the observation inflation is more robust on the changes of system parameters,and improve the accuracy of filtering.