Abstract
Space situational awareness program, for both NEO and debris segments, have to face the challenging problem of accurately managing uncertainties in highly nonlinear dynamical environments. The uncertainties affect all the main phases necessary for the successful realization of the program; i.e., orbital determination, ephemeris prediction, collision probability computation, and collision avoidancemaneuver planning and execution. Since the amount of data that must be processed is huge, efficient methods for the management of uncertainties are required. Differential algebraic (DA) techniques can represent a valuable tool to address this tasks. Differential algebra supplies the tools to compute the derivatives of functions within a computer environment. This technique allows for the efficient computation of high-order expansions of the flow of ordinary differential equations (with respect to initial conditions and/or model parameters) and the approximation of the solution manifold of implicit equations in Taylor series. These two features constitute the building blocks of a set new algorithms for the nonlinear and efficient management of uncertainties. Applications to 1) angles-only preliminary orbit determination 2) propagation of orbital dynamics 3) nonlinear filtering 4) space conjunction prediction 5) robust optimal control are presented to prove the efficiency of DA based algorithms.