SymPKF：参数卡尔曼滤波器动态设计的符号和计算工具箱
SymPKF: a symbolic and computational toolbox for the design of parametric Kalman filter dynamics
摘要：
最近的研究在数据同化导致引入参数卡尔曼滤波器（PKF）：卡尔曼滤波器的实现，其中协方差矩阵近似的参数化协方差模型。在PKF中，预测步骤期间的协方差的动态依赖于协方差参数的预测。因此，参数动力学的设计是至关重要的，而它可以是繁琐的手工做。这一贡献介绍了一个Python包，SymPKF，能够计算PKF动态单变量统计，当协方差模型参数化的方差和局部各向异性的相关性。SymPKF产生PKF动力学的能力显示在一维域上的非线性扩散平流（Burgers方程）和二维域上的线性平流上。PKF动力学的计算是在符号级进行的，但也引入了自动代码生成器来进行数值模拟。最后一个多变量的例子说明了潜在的SymPKF超越单变量的情况下。
英文摘要：
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.
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