Precise real-time orbit estimation using the unscented Kalman filter

The standard Extended Kalman Filter is widely used for nonlinear estimations, its implementation, however, in orbit determination under inaccurate initial conditions and sparse measurement data can lead to an unstable solution. In this paper, an alternative generalization of the Extended Kalman Filter is utilized for robust recursive estimation of the states of an Earth-orbiting satellite. The new nonlinear filter, called the Unscented Kalman Filter, is based on the Unscented Transformation in which a set of sampled sigma points are used to parameterize the mean and covariance of a probability distribution. The performance of the Unscented Kalman Filter in the application is better than that of the Extended Kalman Filter with the same computational complexity, and it generalizes elegantly to nonlinear systems without the burdensome linearization steps, leading to faster and stable convergence properties. Simulation results indicate that the advantages of the Unscented Kalman Filter make it an attractive alternative to the Extended Kalman Filter in the orbit determination.