extending inverse heat conduction method to estimate flight trajectory of a reentry capsule

This study is dedicated to the solution of the inverse heat conduction problem forestimation of the time-varying velocity and altitude profiles regarding the flight trajectory of an earthentrycapsule. four tungsten-rhenium sensors are supposed to be embedded inside the ablative heatshield of the probe, three of which cannot tolerate high-temperature conditions and burn out duringentry and the other one remained intact until the end of the simulation. the conventional levenberg-marquardt method is reinforced by a relaxation scheme to prevent unfavorable severe oscillationsencountered in the inverse iterations. to keep the generality of the method, no prior knowledge onthe thermal condition and surface recession of ablative insulator is utilized in the current estimation.therefore, in the associated direct problem, velocity and altitude profiles are given and the temperaturefield inside the heat shield is determined. accordingly, a solution of the direct problem consists of (i)bow shock calculations in dissociated air (ii) boundary layer solver to compute stagnation heating rate(iii) identification of the thermal response of charring ablative heat shield. it is shown that if the standarddeviation of the temperature measurement error is 5 k, estimation of altitude and velocity are associatedwith approximately 10 and 5 percent normalized error,