Fast method and apparatus for nonlinearly transforming mean and covariance estimates

摘要

A system and a method for estimating the mean and covariance resulting from the application of a given nonlinear function or transformation when applied to a given mean and covariance derived from measurements of a physical system or process. The method comprises selecting a set of points having an arbitrary mean different from the given mean, but with covariance about the given mean equal to that of the given covariance; applying the given nonlinear function to each element of the selected set of points; computing an estimate of the mean of the nonlinearly transformed given mean and covariance; and computing the covariance of the nonlinearly transformed set of points about the estimated mean. The system and method provide an efficient procedure for accurately incorporating nonlinear models of quantities of interest in tracking systems, control mechanisms, and many other related signal processing systems.