For a CKF, the spherical-radial

cubature rule is adopted to implement the integration.

Xu, "Constructing fully symmetric

cubature formulae for the sphere," Mathematics of Computation, Vol.

12] proposed a

cubature Kalman filter (CKF) based on 3-DoF vehicle model to estimate vehicle velocity, sideslip angle, and yaw rate.

Vandewalle, "The construction of

cubature rules for multivariate highly oscillatory integrals," Math.

h] is formed by the standard

cubature formula using the nodes of each element (= lumped mass matrix).

Early works of analysis include such topics as the binomial theorem and as a consequence from it the polynomial theorem, purely analytic proof of the theorem and three problems of rectification, complanation and

cubature ("as a sample of a complete organization of the science of space"), with later analysis and the infinite represented by pure theory of numbers, theory of functions and improvements, and paradoxes of the infinite.

Additional Key Words and Phrases: Automatic integration,

cubature,

cubature rules, error estimation, null rules, symmetry, triangular regions

Kim, A survey of known and new

cubature formulas for the unit disk, Korean J.

The reason is in the fact that interpolating the GF values from the table is much faster than computing the Ewald sums directly (since this has to be done for every pair of source and field triangles in the numerical integration using

cubature formulas.

Compared with other classical nonlinear filters, the high degree

cubature Kalman filter (HCKF) seems to be a good choice to be the substituted local filter, which has superior performance to the extend Kalman filter (EKF), the

cubature Kalman filter (CKF), the unscented Kalman filter (UKF), and the particle filter (PF) [9-12].

The

cubature levels for the numerical integration are defined as in [27], corresponding levels 0, 1, 2, 3, and 4 respectively to 7, 13, 25, 51 and 101 integration points per dimension.

There are also good perspectives in the application to numerical

cubature and to the numerical solution of PDEs by collocation and discrete least squares methods [45].