Abstract: A system and a method for estimating the expected value and covariance of a nonlinear function of a random variable includes the steps of measuring the random variable, generating a discrete distribution of a first set of values for the random variable about the measured value for the random variable which have a predetermined covariance, calculating a second set of values by applying the nonlinear function to the first set of values, and determining the mean and the covariance of the nonlinear function of the measured value based upon the second set of values. The system and the method provide a tractable procedure for accurately estimating the mean and the covariance of a nonlinear function of one or more random variables, which has applications in tracking, process control, and system modelling.