Albers David J, Blancquart Paul-Adrien, Levine Matthew E, Seylabi Elnaz Esmaeilzadeh, Stuart Andrew
Department of Biomedical Informatics, Columbia University, New York, NY 10032.
Department of Pediatrics, Division of Informatics, University of Colorado Medicine, Aurora, CO 80045.
Inverse Probl. 2019;35(9). doi: 10.1088/1361-6420/ab1c09. Epub 2019 Aug 21.
Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it.
集合卡尔曼方法在状态估计和参数估计问题中已成为一种越来越重要的工具。它们的流行源于该方法无需求导的特性，当针对基础状态空间动力学（用于状态估计）或参数到可观测量映射（用于参数估计）有可用的计算机代码时，该方法可轻松应用。在许多应用中，希望以等式或不等式约束的形式对状态或参数施加先验信息。本文为此建立了一个通用框架，描述了一种广泛适用的方法、一种为该方法提供依据的理论以及一组示例说明该方法的数值实验。
