Sigma point filtering for sequential orbit estimation and prediction

The standard extended Kalman filter is widely used for nonlinear estimation. Its implementation, however, in orbit estimation under inaccurate initial conditions and sparse measurements can lead to unstable solutions. In this article, efficient alternatives to the extended Kalman filter are used for recursive nonlinear estimation of the states and parameter of an earth-orbiting satellite. The alternatives, called sigma point filters, include the unscented Kalman filter and the divided difference filter. The sigma point filters have advantages over the extended Kaiman filter in that they do not require the burdensome derivation of the Jacobian and/or Hessian matrix, and they provide more accurate propagation of the state and error co variance matrix than those of the extended Kalman filter. An efficient filter initialization algorithm using the Herrick-Gibbs method is also proposed to provide an initial state and covariance. Simulation results indicate that the advantages of the sigma point filters make these attractive alternatives to the extended Kalman filter in the sequential orbit estimation with the same computational complexity of the extended Kalman filter.