Analytic Method of Propagating a Covariance Matrix to a Maneuver Condition forLinear Covariance Analysis during Rendevous

摘要

This study develops a method for analytically propagating a covariance matrix toa maneuver condition to be used in linear covariance analysis for planning the rendezvous phase of a space mission. With the generalized formulation of a condition transition matrix, an analytic method of propagating an augmented covariance matrix to any scalar terminal maneuver condition is presented. The twenty-six dimensional augmented covariance matrix used in this study includes navigation state errors, state dispersions, and time errors for both the chaser and target craft. The method is first, analytically developed. The vehicles are brought to the desired rendezvous condition by linearizing motion at the maneuver condition point and allowing the time of flight to vary slightly. The analytic propagation technique is then validate by comparison to a stochastic Monte Carlo simulation for the case of several elevation angle conditions which might be used to trigger an initial rendezvous intercept burn. The validity of linearizing the motion about the terminal point is substantiated with the same situation.