This paper addressed the problem of computing practical time-to-go estimation,when constant relative acceleration and measurement distribution were considered . firstly,a time-to-go arithmetic was obtained based on missile and target engagement geometry. The method is a combination of three time-to-go estimate formulations . Then time-to-go estimator was designed by applying the modified gain extended Kalman filter theory.Simulation results show that the proposed estimator can estimate the time-to-go very effectively . The proposed method is simple and straightforward to implement for missiles.