First, a precise and effective Gaussian

cubature transformation-based [19, 20] estimation approach is proposed to compute the time evolution of the debris dispersion by using a moment-matching technique.

In addition,

cubature Kalman filter generates a set of

cubature points propagated by system equations to approximate the posterior estimate which was used.

Smolyak rule [15] is one of the useful tools to generate a small number of

cubature points for high dimensional integral.

In order to further improve the nonlinear Kalman filtering accuracy, this paper proposes a novel spherical simplex-radial

cubature quadrature Kalman filter (SSRCQKF).

In this paper, a nonlinear unknown input observer based on singular value decomposition aided reduced dimension

Cubature Kalman Filter (NUIO based on SVDRDCKF) is discussed.

5th-degree

cubature Kalman filtering algorithm can obtain high accuracy and high stability with low computational cost; thus, it is selected to adaptively adjust the fusion coefficient, kernel parameters, and regression parameters.

analysis, ball, simplex, orthogonal polynomials, approximation,

cubatureDCUTRI: An algorithm for adaptive

cubature over a collection of triangles.

The principle of CKF is to use the spherical-radial rule to get the basic

cubature points and the opposite weights [14].

In order to address the problem that the filtering accuracy of the conventional filters reduces in the case of inaccurate time-varying noise statistic, a noise statistic estimator based adaptive simplex

cubature Kalman filter (ASCKF) is proposed in this paper.

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.

A glance at the contents pages of Stroud's pioneering work [Stroud 1971] is enough to make one realize that the shape of the integration region plays a dominant part in the design of

cubature formulas, and the survey [Cools and Rabinowitz 1993] of developments since then makes it plain that there are only four two-dimensional regions for which there exist a significant variety of

cubature formulas: the square [C.sub.2], the circle [S.sub.2], the unit triangle [T.sub.2], and the plane [E.sub.2].