Guidance, navigation, and control of satellites–especially in the study of rendezvous and formation flight–relies heavily on methods that leverage local linear approximations of dynamical systems and measurement functions. This thesis focuses mainly on cases in which linear approximations are insufficient to solve dynamics, control, or estimation problems. In such cases, we employ tools from numerical multilinear algebra on tensors arising from higher-order Taylor series. The inherently quadratic nature of some quantities, the linear unobservability of some estimation problems, and the need to quantify the performance of linear methods make these higher-order techniques useful in the setting of guidance, navigation,and control.