The kinematic models of the powered phase and the free flight phase of a ballistic missile are different. The accurate estimation of the shutdown state is of great significance to the handover of the tracking information processing mode. Based on radar tracking, the thrust acceleration is used as the eigenvalue to estimate the shutdown state. The observational equation is derived. In view of the nonlinear problem of the observation equation, the recursive least square (RLS) algorithm is used to obtain the recursive estimation of the thrust acceleration by the linearization of random variables. Through the error analysis, the method of calculating the threshold of shutdown state is given. The simulation shows that the estimation method can give the shutdown state results in time and accurately.