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...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.展开更多
By the resultant theory, the E-characteristic polynomial of a real rectangular tensor is defined. It is proved that an E-singular value of a real rectangular tensor is always a root of the E-characteristic polynomial....By the resultant theory, the E-characteristic polynomial of a real rectangular tensor is defined. It is proved that an E-singular value of a real rectangular tensor is always a root of the E-characteristic polynomial. The definition of the regularity of square tensors is generalized to the rectangular tensors, and in the regular case, a root of the Echaracteristic polynomial of a special rectangular tensor is an E-singular value of the rectangular tensor. Moreover, the best rank-one approximation of a real partially symmetric rectangular tensor is investigated.展开更多
This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies...This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.展开更多
基金supported in part by Ministry of Science and Technology of China Through Cooperative Agreement(Grant No.2014CB845303)
文摘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.
文摘By the resultant theory, the E-characteristic polynomial of a real rectangular tensor is defined. It is proved that an E-singular value of a real rectangular tensor is always a root of the E-characteristic polynomial. The definition of the regularity of square tensors is generalized to the rectangular tensors, and in the regular case, a root of the Echaracteristic polynomial of a special rectangular tensor is an E-singular value of the rectangular tensor. Moreover, the best rank-one approximation of a real partially symmetric rectangular tensor is investigated.
文摘This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.
