A Systems Approach to Modeling Uncertain ODE Systems

NASA needs to perform uncertainty analysis of mission performance. One way to perform uncertainty analysis is to use linear covariance techniques. Uncertainty analysis is an important part of all phases of every NASA mission. This type of analysis helps to discover risks, optimize parameters, and validate future success of a system. In this paper, modeling uncertainty with additive zero-mean white noise on process and system outputs is described from a systems modeling approach. Core block diagram algebra rules for uncertain systems that can be used to generalize linear covariance analysis and systematically implement the covariance equations in NASA's Swift Integrated GNC and Mission Analysis (SIGMA) tool. This framework is applied to a rendezvous scenario with a dual inertial physical model and relative GNC systems, demonstrating its flexibility.