The unscented transformation is extended to use extra test points beyond the minimum necessary to determine the second moments of a multivariate normal distribution. The additional test points can improve the estimated mean and variance of the transformed distribution when the transforming function or its derivatives have discontinuities.

No abstract

Boost phase missile tracking is formulated as a nonlinear parameter estimation problem, initialized with an unscented transformation, and updated with a scaled unscented Kalman filter.

No abstract

67 new cubature rules are found for three standard multidimensional integrals with spherically symmetric regions and weight functions, using direct search with a numerical zerofinder. 63 of the new rules have fewer integration points than known rules of the same degree, and 20 are within three points of Möller's lower bound. Most have all positive coefficients and most have some symmetry, including some supported by one or two concentric spheres. They include degree 7 formulas for integration over the sphere and Gaussian-weighted integrals over all space, each in 6 and 7 dimensions, with 127 and 183 points, respectively.