Two nonlinear Kalman filters are evaluated for satellite orbit determination using angles-only data. They are being considered for use in a space situational awareness system that estimates 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). Both filters deal with nonlinear effects that cannot be handled by a conventional Extended Kalman Filter or Unscented Kalman Filter. The GMF consists of a bank of extended Kalman filters whose relative weights are affected by their abilities to fit the measurement data. It includes a re-sampling step 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, over past data samples and dynamic propagation intervals. The filters have been tested using truth-model simulation data for two nearly geosynchronous cases. Reliable convergence and good accuracy can be achieved using once-per-night data arcs that are 20 seconds long. The BSEKF achieves better final accuracy than the GMF, and it uses less computation time.
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