Ballistic coefficient

Abstract: This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.

Abstract: Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however,mostsatelliteshavecomplexgeometries,andamoresophisticatedmethodofcalculatingthedragcoefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation threedimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas–surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani–Lampis–Lordmodels.Resultsshowthatthetwogas–surfaceinteractionmodelscomparewellataltitudes below ∼500 km during solar maximum conditions and below ∼400 km during solar minimum conditions. The differenceindragcoefficientofasphereat ∼800 kmcalculated usingthetwogas–surfaceinteractionmodels is ∼6% during solar maximum and increases to ∼10% during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas–surface interaction models at ∼500 km differs by ∼15% during solar minimum conditions and by ∼2–3% during solar maximum conditions.

Abstract: In this paper, we present a novel computational framework for analyzing the evolution of the uncertainty in state trajectories of a hypersonic air vehicle due to the uncertainty in initial conditions and other system parameters. The framework is built on the so-called generalized polynomial chaos expansions. In this framework, stochastic dynamical systems are transformed into equivalent deterministic dynamical systems in higher dimensional space. Here, the evolution of uncertainty due to initial condition, ballistic coefficient, lift over drag ratio, and atmospheric density is analyzed. The problem studied here is related to the Mars entry, descent, and landing problems. We demonstrate that the polynomial chaos framework is able to predict evolution of uncertainty, in hypersonic flight, with the same order of accuracy as the Monte-Carlo methods but with more computational efficiency.