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Vehicle-borne tracking and position device is used to track LEO satellite. Because of the absence of the target which might be caused by cloud or zenith blind zone, the forecasting data will be used to acquire the target. While orbit prediction has serious errors, the target is always missed. Meanwhile, in its application to the vehicle-borne tracking and position device, due to the base of instability in the tracking process, it will result in significant difference between predicting data and tracking data, so the target will be not tracked rapidly. We applied tracking data to predict satellite orbits by improving Laplace method, and then corrected the error between Predicted data and actual measured data by interpolation method of Lagrange which improves the accuracy of prediction values. The testing data shows the accuracy of predicted data ranging from 3' to 10' for both azimuth and elevation when extrapolated satellite orbit to 7 seconds time.