观测误差协方差估计下的集合鲁棒滤波数据同化方法

王月,摆玉龙,王笛

Ensemble Robust Filtering Data Assimilation Method with Estimation of Observation Error Covariance

Yue Wang,Yulong Bai,Di Wang

表1 EnTLHFR算法描述

Table 1 Description of the ensemble time-local filter with observation error covariance estimation

算法：EnTLHFR

初始化：产生初始化集合成员 $\{x_{o}^{a, i}\}, i = 1, . . ., N$ ，观测矢量 $y_{i}$ ，初始背景协方差矩阵 $P_{0}^{f}$ ，同时确定DBCP诊断的样本数 $N_{s}$ ，假定初始观测误差协方差 $R_{0}$ 。

For $i$ =1:同化步长（ $i = 2 N_{s}$ ）

进行EnTLHF: $x_{i}^{f} = \{x_{i, j}^{f} : x_{i, j}^{f} = M_{j} (x_{i - 1, j}^{a}), j = 1, . . ., n\}$

If $i \leq N_{s}$

$R_{i + 1} = R_{o}$

Else

$R_{i + 1} = E (d_{i}^{a} (d_{i}^{b})^{T})$

End if

EnTLHF预报： ${\overset{ˉ}{x}}_{i}^{b} = {\overset{ˉ}{x}}_{i}^{f} = m e a n (x_{i}^{f})$

$Δ_{i}^{b} = c o v (x_{i}^{b}) + Q_{i}$

背景新息值： $d_{i}^{b} = y_{i} - H ({\overset{ˉ}{x}}_{i}^{b})$

EnTLHF滤波： $[p_{i}^{a}, K_{i}] = E T K F (X_{i}^{b}, Q_{i}, H_{i})$

$G_{i} = (I_{m} - γ_{i} p_{i}^{a} S_{i})^{- 1} K_{i}$

$x_{i}^{a} = {\overset{ˉ}{x}}_{i}^{b} + G_{i} [y_{i} - H ({\overset{ˉ}{x}}_{i}^{b})]$

分析新息值： $d_{i}^{a} = y_{i} - H ({\overset{ˉ}{x}}_{i}^{a})$

If 目标限制函数满足

返回c

Else

警告提示，滤波异常

End if

End for