Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step relies on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial while it can be tedious to do this by hand. This contribution introduces a python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a non-linear diffusive advection (Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.
翻译:数据同化的最近研究导致引入参数卡尔曼过滤器(PKF):实施卡尔曼过滤器,使共变量矩阵以参数化共变量模型相近。在PKF,预测步骤期间共变量的动态取决于对共变量参数的预测。因此,参数动态的设计至关重要,而手动这样做可能会引起争论。这一贡献引入了 python 软件包,SymPKF, 能够为单体统计计算PKF动态, 以及当共变量模型根据差异和关联的局部反异质模型进行参数化时。 SymPKF 生成PKF 动态的能力显示在非线性域 1D 上显示, 和 2D 域的线性适应。 PKF 动态的计算是象征性的, 但自动代码生成器也被引入来进行非数字模拟。最后一个多变量示例显示 SymFate 的Sym- 数字模拟。