Uncertainty analysis of Mars entry flight using time-dependent polynomial chaos

Due to the vehicle's knowledge uncertainty at entry interface caused by the capacity constraint of DSN(Deep Space Network), and difficulties in modeling the Mars atmosphere and the vehicle's atmospheric coefficients exactly, there exists much delivery uncertainty between the actual landing site and the target. To ensure safe landing in the future Mars exploration mission, in which landing on the area with more hazards will be required, it is essential to study the impact of the uncertainties on state trajectories, and to determine the error ellipse of the landing site and the supersonic parachute deployment site. This paper presents a novel approach for the analysis of uncertainty propagation associated with Mars entry problem. In this approach, the Polynomial Chaos are used to approximate the vehicle's states, by introducing the Galerkin projection, the problem is converted to a deterministic dynamical system in higher dimensional space. To avoid breaking down of the generalized polynomial chaos caused by long-time integration, whose essential reason is that the probability density distribution of the solution evolves as a function of time, new stochastic variables and the set of orthogonal polynomials are constructed with respect to the changing probability density as time progresses. The uncertainty sources considered here include initial condition, ballistic coefficient, lift over drag ratio, and the atmospheric density. It is shown mat the results agree very well with Monte-Carlo simulations, but with more computational efficiency.