Approximate Gauss-Newton methods for optimal state estimation using reduced-order models
Approximate Gauss-Newton methods for optimal state estimation using reduced-order models
复制标题
使用降阶模型进行最优状态估计的近似高斯-牛顿方法
DOI：
10.1002/fld.1629
复制
发表时间：
2007
影响因子：
1.8
通讯作者：
Lawless A
中科院分区：
文献类型：
--
作者：
Lawless A
高斯-牛顿 (GN) 方法是一种众所周知的迭代技术，用于求解受动力系统约束的非线性最小二乘问题。此类问题通常出现在系统可能是随机的最优状态估计中。用于天气、海洋和气候系统状态估计的变分数据同化技术目前使用近似全球导航卫星系统方法。 GN 方法解决了一系列受线性化系统约束的线性最小二乘问题。对于非常大的系统，使用模型动力学的低分辨率线性近似来提高算法的效率。我们提出了一种基于控制理论模型简化技术推导低阶系统近似的新方法。我们展示了如何将该技术与 GN 方法结合起来，以更准确地保留动力系统的响应并提高近似 GN 方法的性能。版权所有 © 2007 约翰·威利父子有限公司
The Gauss–Newton (GN) method is a well‐known iterative technique for solving nonlinear least‐squares problems subject to dynamical system constraints. Such problems arise commonly in optimal state estimation where the systems may be stochastic. Variational data assimilation techniques for state estimation in weather, ocean and climate systems currently use approximate GN methods. The GN method solves a sequence of linear least‐squares problems subject to linearized system constraints. For very large systems, low‐resolution linear approximations to the model dynamics are used to improve the efficiency of the algorithm. We propose a new method for deriving low‐order system approximations based on model reduction techniques from control theory. We show how this technique can be combined with the GN method to retain the response of the dynamical system more accurately and improve the performance of the approximate GN method. Copyright © 2007 John Wiley & Sons, Ltd.