GAUSSIAN MIXTURE KALMAN FILTER FOR ORBIT DETERMINATION USING ANGLES-ONLY DATA

A Gaussian mixture nonlinear Kalman filter is developed for satellite orbit determination using angles-only data. It is being developed for a space situational awareness system that must estimate orbits based on sparsely available optical tracking data. The Gaussian mixture framework is used to deal with nonlinear effects that cannot be handled by a conventional extended Kalman filter or an unscented Kalman filter. The Gaussian mixture filter 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 re-sampling 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 filter's initial Gaussian mixture is derived from a short arc of angles-only measurement data and from constraints on the minimum periapsis and the maximum apoapsis. The filter has 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.