Abstract: The state estimation for boost phase is an important issue in the missile defense program, both the target state estimate and the associated error covariance are cuing information for radar in BMD program. In the condition of the space-based observations, the state estimation is the solution of the nonlinear LSE problem. Firstly, the dynamic model for the boost phase based on the net acceleration profile was established. The major difficulties of this problem include the ill-conditioning of the estimation problem due to poor observability of the target motion via LOS measurements, the estimation of the unknown launch time, and the incorporation of inaccurate target thrust profiles to model the target dynamics during the boost phase. Considering the complications mentioned above, a maximum likelihood (ML) estimator based on the Levenberg-Marquardt algorithm that provides both the target state estimate and the associated error covariance was presented. Specially, the explicit derivation of the state estimation under three cases were deduced, and its application conditions were illuminated. Finally, Monte Carlo simulation studies on two typical scenarios were performed. The results indicate that the estimated errors are closed to the CRLB, thus illustrating that the proposed estimator is efficient.