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An acceleration model and a jerk model are proposed in this paper for kinematic state estimation of re-entry ballistic targets. The models proposed here use fully coupled equations of the target kinematics, without assuming any model structure for variations of ballistic coefficient and air density as found in the literature. The novelty of the algorithms lies in the bootstrapped computation of the model parameter γ, which is the ratio of air density and ballistic coefficient, at every time step, utilizing the estimated velocity and acceleration. γ and its time derivatives, thus computed, are used for parameterization of DA and DJ models for estimating position, velocity and acceleration. This makes the algorithms inherently adaptive to the variations of the ballistic coefficient and the air density during the re-entry trajectory. It is demonstrated that the proposed models produce unbiased estimates of target acceleration as opposed to biased estimates from the existing models. [ABSTRACT FROM AUTHOR]