Evaluating Delta-V Dispersions Using Linear Covariance Techniques with Applications to Rendezvous and Docking

One of the attractive advantages of using linear covariance analysis (LinCov) is that it can accurately produce both navigation errors and trajectory dispersions in a fraction of the time comparable to the standard Monte Carlo analysis approach that is traditionally adopted. It also has the capability of generating delta-v dispersions which is perhaps the most influential performance metric since many aspects of a mission design revolve around the anticipated propellant usage. Accurately capturing this key performance criteria using linear covariance techniques has several subtle caveats raising reasonable doubts and a cautious sense of skepticism. This paper outlines multiple approaches of modeling delta-v usage in LinCov, highlights their limitations and advantages, and ultimately compares their corresponding results to the actual Monte Carlo performance. The theory is also extended to reliably account for an arbitrary thruster configuration and the resultant propellant consumptions due to both translational burns and attitude maneuvers. This provides near instant insight into the impacts of thruster layout design and different vehicle mass properties. These derived techniques are applied and verified using an NRHO rendezvous and docking scenario consistent with upcoming NASA Artemis missions for Orion.