A UKF based design method for lunar free-return trajectories

A method based on unscented Kalman filter parameter estimation is proposed for the design of lunar free-return trajectories. The method avoids calculating the Jacobian matrix and obtains large convergence ability compared with the common differential-correction method. Given that the initial estimate of the free-return trajectory is only required to be generated under the two-body Earth–spacecraft model, the difficulty of guessing a good initial estimate is greatly reduced. Through converting the original problem to a parameter estimation representation, the method is used to find the converged final solution that satisfies the constraints at injection, perilune, and Earth-entry interface under a high-fidelity gravitational model. In addition to its deceptively simplicity, the method proves to be quite effective through numerical examples in finding the solution to lunar free-return trajectories within a few iterations with great numerical accuracy.