Thermospheric Density Model Calibration Based On Empirical Orthogonal Function

The force produced by thermospheric density is the largest non-gravitational perturbation acting on low orbit space-crafts,which has great influence to space missions such as orbit determination,orbit prediction,re-entry operations of low Earth orbit objects.With the development of manned space career in our country,it is difficult for existing thermospheric density models to satisfy space mission requirements because of the model errors on the order of 15%?20%.Focusing on the method of thermospheric density model calibration,the main contributions of this thesis are as follows.First,inspired by the idea of calibrating model density with temperature parameter corrections,the analytical partial derivative between the model density logarithm and the temperature parameters is constructed for model calibration in consideration of the bias in Jacchia-Roberts empirical thermospheric density model.According to the non-linearity of model about temperature parameters,the iterative process of parameter corrections is obtained by using the calibration algorithm of thermospheric density model,which lays the foundation for calibration of thermospheric density model.Second,a new method for thermospheric density model calibration based on empirical orthogonal function(EOF)is put forward and compared with the traditional spherical harmonics(SH).Results show that more than 85% and 80% variations of temperature parameter corrections are involved in the first 4 EOFs and the first 9 SH expansion functions.The first EOF reflects the overall bias of temperature corrections.The coefficients corresponding to the second to fourth EOF show that the temperature corrections have diurnal periodicity,which is also reflected in the SH coefficients.Jacchia-Roberts is calibrated by the reconstructed temperature corrections using the first 4 EOFs and the first 4SH expansion functions,and the calibrated density deviations of Jacchia-Roberts reduce by 9.06% and 3.57%,respectively.The results show that EOF method is better than SH method in the efficiency of temperature parameter corrections and the improvement of model accuracy.Third,three methods for the nonlinear least-squares problem are studied to handle the nonlinear relationship between thermospheric density models and temperature parameters.The effects of Gauss-Newton(G-N)method,damped Gauss-Newton(damped G-N)method and Levenberg-Marquardt(L-M)algorithm for the calculation of temperature parameter corrections are compared.G-N method has obvious non-convergence at some sampling points.An analysis indicates the nonlinearity in Jacchia-Roberts with respect to temperature parameters is the reason of non-convergence.The calculations of damped G-N method and L-M algorithm overcome the non-convergence phenomenon of G-N method effectively,and average standard deviation of the modified model are both reduced approximately by 13.5%.Damped G-N method and L-M algorithm have similar average iteration times,which are 2.8 and 2.9 respectively.Due to the ability of adjusting iterative descent direction and stronger adaptability in L-M algorithm,it has more advantages than the other two algorithms in solving the nonlinear least-squares problem of temperature parameter corrections in thermospheric model.