Minimizing the Effects of Impulsive Orbit Maneuver Uncertainty

Abstract

The terminal state error under impulse orbit maneuver uncertainty is minimized using the linear covariance method. A new actuation-error model is proposed for practical engineering application, which requires that the thrust direction be aligned with the impulse vector. The polar angle in the error model can be adjusted to reduce the terminal error. This paper studies two impulse-maneuver problems, including short-range orbit rendezvous and translunar midcourse correction. First the state transition matrices for the two problems are provided. Then the control error matrix is derived under impulse-magnitude and impulse-direction errors. The terminal linear covariance matrix is obtained by considering both navigation and actuation errors. Finally, the optimal polar angle is numerically solved by the golden-section search. Numerical examples are provided to verify the proposed method for the analytical linear covariance matrix and the optimal polar angle.