In this paper, the construction and effectiveness of the so-called Cubature Kalman Filter (CKF) is revisited, as well as its extensions for higher degrees of precision. In this sense, some stable (with respect to the dimension) cubature rules with a quasi-optimal number of nodes are built, and their numerical performance is checked in comparison with other known formulas. All these cubature rules are suitably placed in the mathematical framework of numerical integration in several variables. A method based on the discretization of higher order partial derivatives by certain divided differences is used to provide stable rules of degrees $d=5$ and $d=7$, though it can also be applied for higher dimensions. The application of these old and new formulas to the filter algorithm is tested by means of some examples.

在本文中，重新讨论了所谓的Cubature卡尔曼滤波器（CKF）的结构和有效性，以及它的扩展以实现更高的精度。从这个意义上讲，建立了一些具有准最优节点数目的稳定（相对于维数）培养规则，并与其他已知公式进行了比较，验证了它们的数值性能。所有这些培养规则都适当地放置在几个变量的数值积分的数学框架中。一种基于通过某些划分的差异对高阶偏导数进行离散化的方法来提供稳定的度数规则$d=5$ 和 $d=7$，尽管它也可以应用于更大的尺寸。通过一些示例测试了这些新旧公式在过滤器算法中的应用。