论文标题
参数卡尔曼过滤器预测提交的边界条件
Boundary Conditions for the Parametric Kalman Filter forecast submited
论文作者
论文摘要
本文是对参数卡尔曼滤波器（PKF）的探索的贡献，该滤波器是卡尔曼滤波器的近似值，其中误差协方差通过协方差模型近似。在这里，我们关注从局部相关性的方差和各向异性参数化的协方差模型，并且其参数动力学为完整的误差协调动力学提供了代理。对于此协方差模型，我们旨在提供边界条件，以在PKF预测有限域的预测中指定时，重点介绍了Dirichlet和Neumann条件，以便它们为物理动力学规定。提出了用于传输方程和在有界的1D域上的异质扩散方程的集合验证。该整体验证需要指定填充边界扰动所需的自动相关时间尺度，从而导致规定的不确定性特征。数值模拟表明，PKF能够从对边界上适当扰动的预测合奏中诊断出的不确定性，这表明了PKF在预测不确定性时处理边界的能力。结果导致对物理动力学的条件意味着方差和各向异性的差异条件。代码可从https://github.com/opannekoucke/pkf-boundary获得
This paper is a contribution to the exploration of the parametric Kalman filter (PKF), which is an approximation of the Kalman filter, where the error covariances are approximated by a covariance model. Here we focus on the covariance model parameterized from the variance and the anisotropy of the local correlations, and whose parameters dynamics provides a proxy for the full error-covariance dynamics. For this covariance model, we aim to provide the boundary condition to specify in the prediction of PKF for bounded domains, focusing on Dirichlet and Neumann conditions when they are prescribed for the physical dynamics. An ensemble validation is proposed for the transport equation and for the heterogeneous diffusion equation over a bounded 1D domain. This ensemble validation requires to specify the auto-correlation time-scale needed to populate boundary perturbation that leads to prescribed uncertainty characteristics. The numerical simulations show that the PKF is able to reproduce the uncertainty diagnosed from the ensemble of forecast appropriately perturbed on the boundaries, which show the ability of the PKF to handle boundaries in the prediction of the uncertainties. It results that Dirichlet condition on the physical dynamics implies Dirichlet condition on the variance and on the anisotropy. Codes are available at https://github.com/opannekoucke/pkf-boundary
