Abstract: A method of estimating the navigational state of a system entails acquiring observation data produced by noisy measurement sensors and providing a probabilistic inference system to combine the observation data with prediction values of the system state space model to estimate the navigational state of the system. The probabilistic inference system is implemented to include a realization of a Gaussian approximate random variable propagation technique performing deterministic sampling without analytic derivative calculations. This technique achieves for the navigational state of the system an estimation accuracy that is greater than that achievable with an extended Kalman filter-based probabilistic inference system.

Abstract: 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.

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.