Research On Clock Error Prediction Based On Spline Interpolation And Kalman Filter

GPS time service is widely used all around the world because of its merits of broad coverage area and high precision. Accurate orbit information is the basis of precision positioning and precision time service, therefore how to acquire the accurate orbit information and the receiver clock bias is the key technology of GPS time service research and the emphasis of this paper.For general users, the satellite coordinates are calculated by fixed formulas with the broadcast ephemeris parameters of satellite navigation message received by the receiver. This calculation has a complicated process and it require lots of memories so it could affect the efficiency of calculation. Currently, using interpolation of broadcast ephemeris to acquire accurate satellite coordinates is the common solution. At first, algorithms of Lagrange interpolation and cubic spline interpolation are introduced in this paper, aiming at the problem that the boundary condition of spline interpolation is difficult to get, a method combined with spline interpolation and Lagrange interpolation is proposed, and this method is used in interpolation of ephemeris provided by IGS to get satellite orbit data, then the precision of this algorithm is given and the influence of interpolation order on precision is analyzed. On this basis, the receiver clock bias is calculated by the satellite orbit parameters which has been interpolated. Errors that affects the receiver clock bias can be classified into two categories including system errors and random errors according to their properties. System errors can be eliminated with empirical model. Random errors is hard to be modeled and the method to eliminate random errors by Kalman filter is proposed in this paper. Because of the fact that the initial parameters has great effects on the filtering results, the Kalman filter initial parameters are derived and analyzed. Finally, Kalman filtering is researched based on the receiver clock bias obtained by calculation of interpolated satellite orbit data. Experiment results show that the clock bias prediction method of this paper can improve the precision and stability of receiver clock.In the end of this paper, the research work will be summarized and the outlook of the future work will be given.Through the experimental result, some meaningful conclusions are obtained:By interpolation, ephemeris data whose sampling rate fit need can be acquired and the interpolation error is in the allowable range. For receiver’s high speed data collection, this method can be the reference to raise the efficiency and low the computing complexity.The Lagrange interpolation algorithm is suitable for those application which needs no large amounts of data and it can archive high precise. The spline interpolation algorithm is suitable for the application whose boundary condition is easily to obtained and the applications that need high speed computing.Kalman filter can estimate the real value of signals from the signals with noise.The experimental result shows that by Kalman filtering the receiver’s clock difference can be predicted precisely.By this way,time service precision will be improved.