Nonlinear effects in the correlation of tracks and covariance propagation

Even though there are methods for the nonlinear propagation of the covariance the propagation of the covariance in current operational programs is based on the state transition matrix of the 1st variational equations, thus it is a linear propagation. If the measurement errors are zero mean Gaussian, the orbit errors, statistically represented by the covariance, are Gaussian. When the orbit errors become too large they are no longer Gaussian and not represented by the covariance. One use of the covariance is the association of uncorrelated tracks (UCTs). A UCT is an object tracked by a space surveillance system that does not correlate to another object in the space object data base. For an object to be entered into the data base three or more tracks must be correlated. Associating UCTs is a major challenge for a space surveillance system since every object entered into the space object catalog begins as a UCT. It has been proved that if the orbit errors are Gaussian, the error ellipsoid represented by the covariance is the optimum association volume. When the time between tracks becomes large, hours or even days, the orbit errors can become large and are no longer Gaussian, and this has a negative effect on the association of UCTs. This paper further investigates the nonlinear effects on the accuracy of the covariance for use in correlation. The use of the best coordinate system and the unscented Kalman Filter (UKF) for providing a more accurate covariance are investigated along with assessing how these approaches would result in the ability to correlate tracks that are further separated in time.