Variable node drag parameterization for reentry trajectory estimation

A numerical parameter optimization technique is used to determine the piecewise continuous polynomial approximation to the drag coefficient history that produces a re-entry trajectory that best matches radar data in a weighted least-squares sense. The drag coefficient is parameterized in terms of node point locations, and polynomial coefficients or function values at the nodes. Estimation of node locations for drag coefficient histories using simulated radar data has reduced data residuals by almost one-half through improved approximation of the sharp rise in drag coefficient caused by boundary layer transition. Nomenclature a = parameters which determine node spacing C.D = drag coefficient / = vector of first derivatives of state equations F = function for data fitting example g = function relating states to observations J — quadratic form to be minimized m = total number of parameters to be estimated N = number of observations n — number of points at which function is estimated / =time W — weighting matrix x = state variables y = observed variables e = error between observed and estimated variables (•) = differentiation with respect to time