Aiming at overcoming the weakness that the traditional prediction model based on Kalman filtering does not provide the error estimate of the position prediction, we put forward an extended self-adaptive Kalman filtering model, which can show us the state equation of the prediction errors about the position, velocity and acceleration of the object described. This method realizes the purpose on the effectively error estimate of the position prediction. Simulation experiments indicate that our method not only inherits the good adaptability for mechanical motion of the original but also preferably provides the way on how to estimate the error of the position prediction; therefore, the shortage of the traditional model could be covered effectively by the way presented, which provides a higher speed and accuracy of the estimation.