We develop an algorithm based on the nudging data assimilation scheme for the concurrent (on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial differential equations in which the state is partially observed. The algorithm takes advantage of the error that results from nudging a system with incorrect parameters with data from the true system. The intuitive nature of the algorithm makes its extension to several different systems immediate, and it allows for recovery of multiple parameters simultaneously. We test the method on the Kuramoto-Sivashinsky equation in one dimension and demonstrate its efficacy in this context.

翻译：我们开发了一种基于裸数据同化办法的算法,用于同时(在飞行时)估算一个部分观察到状态的进化分离部分偏差方程式系统的标量参数。算法利用了一个错误,这个错误产生于一个带有错误参数的系统,并附有来自真实系统的数据。算法的直觉性质使它能立即扩展到几个不同的系统,并允许同时恢复多个参数。我们在一个维度上测试Kuramoto-Sivashinsky方程式的方法,并在此范围内展示其效力。