Inertial navigation system(INS) errors increase with time due to inertial sensor errors, and therefore it is desired to combine INS with external aids such as GPS. However GPS informations have a randomly abrupt jump due to a sudden corruption of the received satellite signals and environment, and moreover GPS can`t provide navigation solutions. In this paper, smoothing and prediction schemes are proposed for GPS`s jump or unavailable GPS. The smoothing algorithm which is designed as a scalar adaptive filter, smooths abrupt jump. The prediction algorithm which is proved by Schuler error model of INS, estimates INS error in appropriate time. The outputs of proposed algorithm apply stable measurements to GPS aided INS Kalman filter. Simulations show that the proposed algorithm can effectively remove measurement jump and predict INS error.