Generation of random points uniformly distributed in hyperellipsoids

A precise and efficient algorithm for generating random points uniformly distributed in an arbitrary hyperellipsoid of dimension n is presented. Both the spherical coordinate and the Cartesian coordinate versions are given. Such random points are essential in the Monte Carlo method for numerical integration and in Monte Carlo simulations for the study and design of stochastic systems, especially in target tracking. The algorithm can also be used to generate random points uniformly distributed in a sector of a hyperellipsoid efficiently