The performance of ensemble‐based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are not usually known and have to be inferred. Many approaches have been proposed to tackle this problem, including fully Bayesian, likelihood maximization and innovation‐based techniques. This work focuses on maximization of the likelihood function via the expectation–maximization (EM) algorithm to infer the model error covariance combined with ensemble Kalman filters and particle filters to estimate the state. The classical application of the EM algorithm in a data assimilation context involves filtering and smoothing a fixed batch of observations in order to complete a single iteration. This is an inconvenience when using sequential filtering in high‐dimensional applications. Motivated by this, an adaptation of the algorithm that can process observations and update the parameters on the fly, with some underlying simplifications, is presented. The proposed technique was evaluated and achieved good performance in experiments with the Lorenz‐63 and Lorenz‐96 dynamical systems designed to represent some common scenarios in data assimilation such as nonlinearity, chaoticity and model mis‐specification.

中文翻译：

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使用在线期望最大化算法的粒子和集合卡尔曼滤波器中的模型误差协方差估计

基于集合的数据同化技术的性能，可从部分观测值估算动力学系统的状态，这在很大程度上取决于模型动力学和观测值的规定不确定性。这些通常是未知的，必须进行推断。已经提出了许多解决此问题的方法，包括完全贝叶斯方法，似然最大化和基于创新的技术。这项工作着重于通过期望最大化（EM）算法来推论似然函数，以推断模型误差协方差，并结合集合卡尔曼滤波器和粒子滤波器来估计状态。EM算法在数据同化上下文中的经典应用包括过滤和平滑固定的观察值批处理，以完成单个迭代。在高维应用程序中使用顺序过滤时，这是一个不便之处。以此为动机，提出了一种算法的改编，该算法可以处理观察并实时更新参数，并且具有一些基本的简化方法。在采用Lorenz-63和Lorenz-96动力学系统进行的实验中，对所提出的技术进行了评估，并取得了良好的性能，该动力学系统旨在表示数据同化中的一些常见情况，例如非线性，混沌和模型错误指定。