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, sorne 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=s 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 sorne examples.
