非线性观测算子的集合卡尔曼滤波的改进

IMPROVEMENT ON ENSEMBLE KALMAN FILTER OF NONLINEAR OBSERVATIONAL OPERATOR

在带有线性观测算子的集合卡尔曼滤波中,对预报误差方差阵比较客观的调整是用与时间相依的因子对其进行膨胀调整,然后用极大似然方法去估计膨胀因子.若观测算子是非线性的,新息的似然函数不易表示,从而膨胀方法不能直接套用.我们通过对非线性观测算子的线性逼近,得到似然函数的近似表达式,进而实现对预报误差方差阵的膨胀调整.数据模拟表明这种方法预报精度更高,更加稳健,效果远好于传统的非线性集合卡尔曼滤波方法.

In ensemble Kalman filter of linear observational operator, relatively objective adjustment on forecast error eovariance matrix is on-line inflation adjustment followed by inflation factor optimization by minimizing --21ogqikelihood of observation-minus-forecast residuals. If observational operator is nonlinear, --2log-likelihood are easily expressed, therefore inflation adjustment cannot be applied directly. We derive approximate expression of --2log-likelihood through linear approximation of observational operator, followed by inflation adjustment on foreeast error eovarianee matrix. Data simulation indicated that this proposed method is more accurate and more robust, much better than traditional ensemble Kalman filter of nonlinear observational operator.