Seminars

Two nonlinear Kalman filters are developed and evaluated for satellite orbit determination using angles-only data. They are being considered for use in a space situational awareness system that must estimate orbits based on sparsely available optical tracking data. One filter is a Gaussian Mixture Filter (GMF). The other is a Backward-Smoothing Extended Kalman Filter (BSEKF),which is also known as a Moving-Horizon Estimator (MHE). Both filters seek to deal with nonlinear effects that cannot be handled by a conventional extended Kalman filter or an unscented Kalman filter. The GMF consists of a bank of extended Kalman filters whose relative weights are affected by their relative abilities to fit the measurement data. It includes a resampling step between the dynamic propagation and the measurement update that enforces an upper bound on each mixand's covariance. This bound enables the algorithm to maintain a good approximation of the underlying Bayesian conditional probability density function despite nonlinearities. The BSEKF performs iterative maximum a posteriori nonlinear smoothing over the present data sample and, retrospectively, past data samples and dynamic propagation intervals. Both filters are initialized using a Gaussian mixture that has been derived from a short arc of angles-only measurement data and from constraints on the minimum periapsis and the maximum apoapsis. The filters have been tested using truth-model simulation data for several nearly geosynchronous cases. Reliable convergence and good accuracy can be achieved using once-per-night data arcs that are only 20 seconds long. The new GMF is able to operate with many fewer mixands than another GMF that has been proposed for this problem. The BSEKF is better than the GMF at handling an increased initial uncertainty that results from looser initial bounds on the minimum periapsis and the maximum apoapsis. The two filters’ computation time requirements are similar, although the BSEKF enables reduced computational effort in the algorithm that performs filter initialization based on a single short data arc.