Estimating the ballistic coefficient of a re-entry vehicle

Theoretical bounds for estimating the ballistic coefficient of a ballistic object during the re-entry phase have been addressed. One essential characteristic of the vehicle trajectory is its deceleration when it reaches dense atmospheric layers. The intensity of the phenomenon is proportional to a scalar, called the ballistic coefficient. This leads to an highly nonlinear time-varying dynamic. To understand the dimensioning parameters for estimating the ballistic coefficient, accurate approximations of the Fisher information matrix are developed. The main result is a closed-form expression of a lower bound for the variance of the ballistic coefficient estimate. Notations † Let S be the object cross-section, CX its drag coefficient and M its mass, † the ballistic coefficient b is the product CxS/m and is expressed in m kg, † go 1⁄4 29.8 ms is the gravitational acceleration (at ground level), † alt is the altitude; alt W y in the coordinate system of the Fig. 1, † the atmospheric density (r(y)) is modelled by an exponential law: r (y) 1⁄4 r0 exp [ y=cr] (in kg m), with cr 1⁄4 7000 m and r0 1⁄4 1.2 kg m, † q( y) W 1 2 r( y)n is the dynamic pressure, † r denotes the target range and v its velocity, † FIM: Fisher information matrix; CRB: Cramér-Rao bound, RV: re-entry vehicle, LOS: line of sight, † det: determinant; A: A transposed.