Efficient uncertainties propagation based on differential algebra Seminar

The problem of nonlinear uncertainty propagation represents a crucial issue in spaceflight dynamics since all practical systems - from vehicle navigation to orbit determination or target tracking - involve nonlinearities of one kind or another. Differential algebra technique is here presented as a tool to tackle this problem. Differential algebra supplies the tools to compute the derivatives of functions within a computer environment. More specifically, by substituting the classical implementation of real algebra with the implementation of a new algebra of Taylor polynomials, any function f of n variables is expanded into its Taylor polynomial up to an arbitrary order k. This technique allows 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 of efficient algorithms for the nonlinear 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 the proposed technique.