A More Reliable Orbit Initialization Method for LEO Precise Orbit Determination Using GNSS

Precise orbit determination (POD) using GNSS has been rapidly developed and is the mainstream technology for the navigation of low Earth orbit (LEO) satellites. The initialization of orbit parameters is a key prerequisite for LEO POD processing. For a LEO satellite equipped with a GNSS receiver, sufficient discrete kinematic positions can be obtained easily by processing space-borne GNSS data, and its orbit parameters can thus be estimated directly in iterative manner. This method of direct iterative estimation is called as the direct approach, which is generally considered highly reliable, but in practical applications it has risk of failure. Stability analyses demonstrate that the direct approach is sensitive to oversized errors in the starting velocity vector at the reference time, which may lead to large errors in design matrix because the reference orbit may be significantly distorted, and eventually cause the divergence of the orbit parameter estimation. In view of this, a more reliable method, termed the progressive approach, is presented in this paper. Instead of estimating the orbit parameters directly, it first fits the discrete kinematic positions to a reference ephemeris in the form of the GNSS broadcast ephemeris, which construct a reference orbit that is smooth and close to the true orbit. Based on the reference orbit, the starting orbit parameters are computed in sufficient accuracy, and then the final orbit parameters are estimated with a high accuracy by using discrete kinematic positions as measurements. The stability analyses show that the design matrix errors are reduced in the progressive approach, which would assure more robust orbit parameter estimation than the direct estimation approach. Various orbit initialization experiments are performed on the KOMPSAT-5 and FY3C satellites. The results have fully verified the high reliability of the proposed progressive approach.

INVESTIGATION OF THE DEFECT STRUCTURE, OPTICAL AND EPR SPECTRA FOR CdS: Ti2+ AND CdSe: Ti2+ CRYSTAL

The optical spectral band positions and spin-Hamiltonian parameters (g factors g‖, g⊥ and zero-field splitting D) of CdS : Ti 2+ and CdSe : Ti 2+ crystals are calculated from the complete diagonalizaion (of energy matrix) method based on a two-spin-orbit parameter model for 3d2 ions in trigonal symmetry. In the model, both the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central 3d2 ions and that of ligand ions are included. The crystal field parameters used in the calculations are obtained from the superposition model which enables correlation of the optical and EPR spectral data with the defect structure of the studied paramagnetic impurity centers in crystals. From the calculations, the defect structures of Ti 2+ centers in CdS : Ti 2+ and CdSe : Ti 2+ are acquired, the signs of zero-field splittings D are suggested, and the optical band positions and spin-Hamiltonian parameters are explained. The results are discussed.

The Effect of C22 on Orbit Energy and Angular Momentum

The effect of the C22 gravity field term on a particle is evaluated analytically over one orbit to find the change in orbit energy and angular momentum as an explicit function of the orbital inclination, argument of pericenter, longitude of the ascending node, orbit parameter and eccentricity. Changes in orbit energy and angular momentum are shown to be proportional to a family of integrals which can be parameterized in terms of eccentricity and non-dimensional pericenter radius.

A COMPARISON OF SPIN-ORBIT PARAMETERS

Hartree–Fock results for some spin-orbit parameters are presented. The calculations are based on the Blume and Watson (1962) expression for the spin-orbit parameter, derived on the assumption that the atomic wave function is antisymmetric.The results are compared with experimental values and it is shown that the earlier conclusions concerning the accuracy of the spin-orbit parameter for 3p and 3d electrons are not valid. The results are also compared with Hartree–Fock–Slater values based on a simplified definition.