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遥感技术与应用  2021, Vol. 36 Issue (5): 1111-1120    DOI: 10.11873/j.issn.1004-0323.2021.5.1111
数据与图像处理     
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
西北师范大学物理与电子工程学院,甘肃 兰州 730070
Ensemble Robust Filtering Data Assimilation Method with Estimation of Observation Error Covariance
Yue Wang(),Yulong Bai(),Di Wang
College of Physics and Electrical Engineering,Northwest Normal University,Lanzhou 730070,China
 全文: PDF(3838 KB)   HTML
摘要:

在数据同化方法中,观测误差协方差矩阵是相关的,且与时间和状态有一定的依赖性。针对这种相关特性,将鲁棒滤波方法与观测误差协方差估计方法相结合,得到随状态时间变化的观测误差协方差,提出一种带有观测误差估计的鲁棒数据同化新方法,更新观测误差协方差,改善估计效果。从分析误差协方差,转移矩阵特征值放大等角度优化同化方法。利用非线性Lorenz-96混沌系统,对三种不同优化角度下带有观测误差估计的鲁棒滤波和原鲁棒滤波方法的鲁棒性和同化精度进行评估,并比较分析了两种方法在模型误差、观测数目和性能水平系数变化时的性能。结果表明:观测误差估计技术能够提高状态估计的精确性,带有观测误差估计的鲁棒滤波对系统参数变化具有较好的鲁棒性。

关键词: 集合鲁棒滤波观测误差协方差Lorenz-96混沌系统鲁棒性    
Abstract:

In the data assimilation method, the observation error covariance matrix is correlated and dependent on time and state. in view of such correlation characteristics, the robust filtering method is combined with the estimation of observation error covariance to obtain the time-varying covariance of observation error, and the robust data assimilation method with observation error estimation is proposed to update the observation error covariance and improve the estimation performance. In this work, nonlinear lorenz-96 chaotic system is used to evaluate the robustness and assimilation accuracy of robust filtering with observation error estimation and original robust filtering under three different optimization methods. The performance of the two methods is compared and analyzed when the model error, the number of observations and the performance level coefficient change. The results show that the observation error estimation technique can improve the accuracy of the state estimation, and the robust data assimilation with the observation error estimation is more robust on the change of system parameters.

Key words: Ensemble robust filtering    Observation error covariance    Lorenz-96 model    Robustness
收稿日期: 2020-08-08 出版日期: 2021-12-07
ZTFLH:  TP79  
基金资助: 国家自然科学基金项目(41861047);西北师范大学科研能力提升团队项目(NWNU-LKQN-1706)
通讯作者: 摆玉龙     E-mail: wangyue951210@gmail.com;yulongbai@gmail.com
作者简介: 王月(1995-),女,甘肃皋兰人,硕士研究生,主要从事数据同化观测误差方面的研究。E?mail: wangyue951210@gmail.com
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引用本文:

王月,摆玉龙,王笛. 观测误差协方差估计下的集合鲁棒滤波数据同化方法[J]. 遥感技术与应用, 2021, 36(5): 1111-1120.

Yue Wang,Yulong Bai,Di Wang. Ensemble Robust Filtering Data Assimilation Method with Estimation of Observation Error Covariance. Remote Sensing Technology and Application, 2021, 36(5): 1111-1120.

链接本文:

http://www.rsta.ac.cn/CN/10.11873/j.issn.1004-0323.2021.5.1111        http://www.rsta.ac.cn/CN/Y2021/V36/I5/1111

算法:EnTLHFR

初始化:产生初始化集合成员xoa,i,i=1,...,N,观测矢量yi,初始背景协方差矩阵P0f,同时确定DBCP诊断的样本数Ns,假定初始观测误差协方差R0

Fori=1:同化步长(i=2Ns

进行EnTLHF:xif=xi,jf:xi,jf=Mj(xi-1,ja),j=1,...,n

IfiNs

Ri+1=Ro

Else

Ri+1=E(dia(dib)T)

End if

EnTLHF预报xˉib=xˉif=mean(xif)

Δib=cov(xib)+Qi

背景新息值dib=yi-H(xˉib)

EnTLHF滤波:[pia,Ki]=ETKF(Xib,Qi,Hi)

Gi=(Im-γipiaSi)-1Ki

xia=xˉib+Gi[yi-H(xˉib)]

分析新息值: dia=yi-H(xˉia)

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

表1  EnTLHFR算法描述
图1  EnTLHFR随着性能水平系数变化的RMSE
图2  强迫参数F=6(a),8(b),9(c)时,在分析协方差放大条件下,EnTLHF和EnTLHFR的RMSE均值
图3  当观测误差协方差为单位阵时,基于观测角度构建的协方差放大条件下,EnTLHF和EnTLHFR的AES值
图4  当观测误差协方差为RT时,基于观测构建的协方差放大条件下,EnTLHF和EnTLHFR的AES值
图5  强迫参数F=6,8,9及不同的c值下,转移矩阵特征值放大条件下,EnTLHF和EnTLHFR的RMSE时间均值
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