Gravitational Spectrum Analysis And State Estimation Methods For Satellite-to-Satellite Tracking Mission

In this dissertation there are mainly two problems discussed. One is the spectrum analysis theory of gravity vector of satellites in high-low or low-low mode, the other is the derivation of new state-estimation methods based on the Extended Kalman Filter. The main work and research are listed as follows.The aim of spectrum analysis is to determine the very parts of the Earth's gravitational field that have the strongest effect on the orbit of an artificial satellite. To attain this goal, this dissertation presents a spectrum analysis method which is based on an analytical Fourier series analysis of the commonly used spherical harmonic series expansion which is used for the representation of the Earth's gravitational field. By means of the spectrum expansion the connection between the gravity potential coefficients and the frequencies in the field's representation is determined.Within the Cartesian coordinates framework, recursive formulae for the computation of not only gravitational vector but also the gravitational tensor are derived which have more stable numerical performance than direct formulae. And the transformation of both gravitational vector and tensor is also discussed in detail.The computation of gravitational acceleration vectors of a satellite from its position and velocity observables, as well as its orbit determination, can be reduced to a state estimation problem for nonlinear systems. Firstly, a state-space model for satellite gravity observation system is set up and its observability is analyzed. Then, as far as state estimation of highly non-linear systems like the satellite gravity observation system is concerned, this dissertation is also dedicated to improve the existing Extended Kalman Filter. There are mainly two new state estimation methods put forward: Sigma Point Kalman Filter and Central Difference Kalman Filter. Although these two new methods are similar to the Extended Kalman Filter, they overcome its inherent defects through statistical linearization approximation, and thus gain higher accuracy, more stable numerical stability, while the computation cost can be kept low by means of efficient linear algebraic techniques. And the methods are essentially same and both can be called the Sigma Point Kalman Filter. Results of experiments show that the new methods can be used in place of the Extended Kalman Filter in most applications.Base on the above-mentioned spectrum analysis and state estimation methods, the dedicated gravitational field mission, GRACE, serves as an example with special conditions highlighted that arise for low earth orbit missions. The determination of the gravitational acceleration vectors acting on the GRACE satellites along the orbit from the observables position and velocity is performed by means of the Sigma Point Kalman Filter for filtering and parameter estimation for non-linear systems. The results can serve as reference for practical data processing.