Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter design. An augmented state filter is also developed to deal with unknown significant measurement biases. Simulations are conducted to analyze the effects of initial errors, data-sampling periods, orbital heights, attitude and gradiometer noise levels, and measurement biases. Results show that the filter performs well with additive white noise observation errors. Degraded observability for the along-track position is found for the augmented state filter. Real flight data from the GOCE satellite are used to test the algorithm. Radial and cross-track position errors of less than 100 m have been achieved.
We consider a system composed of two different types of particles that have different radii, but equal density. Both particles experience gravity and a linear drag force from the interstitial fluid. They are excited by a boundary that vibrates with high frequency and adds sufficient energy that the particles near the boundary become highly dilated. For moderate energy input rates we show that a single large particle introduced into a large number of small particles will rapidly move to a fixed height and remain approximately stationary. In particular, the large particle will never come into contact with the vibrating base. If there are a large number of large particles, then this behavior leads to a very distinct segregation in which the large particles are sandwiched between two layers of small particles. We show that this behavior occurs as a direct result of non-equilibrium effects and develop a simple phenomenological model that gives good predictions of the height at which the sandwiched layer occurs.
An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of
Rapid satellite-to-site visibility determination is of great significance to coverage analysis of satellite constellations as well as onboard mission planning of autonomous spacecraft. This paper presents a novel self-adaptive Hermite interpolation technique for rapid satellite-to-site visibility determination. Piecewise cubic curves are utilized to approximate the waveform of the visibility function versus time. The fourth-order derivative is used to control the approximation error and to optimize the time step for interpolation. The rise and set times are analytically obtained from the roots of cubic polynomials. To further increase the computational speed, an interval shrinking strategy is adopted via investigating the geometric relationship between the ground viewing cone and the orbit trajectory. Simulation results show a 98% decrease in computation time over the brute force method. The method is suitable for all orbital types and analytical orbit propagators.
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