论文标题
用于计算信号传播时间的椭圆积分，由卫星在一个轨道上发射和接收
Elliptic Integrals for Calculation of the Propagation Time of a Signal, Emitted and Received by Satellites on One Orbit
论文作者
论文摘要
信号的传播时间是，沿GPS（或Glonass）卫星构造沿椭圆形轨道卫星移动而发出的传播时间是该理论的非常重要的成分，基于无效锥的形式和对一般相对论的影响。对于沿平面椭圆轨道绕的卫星而言，已经证明，卫星之间信号的传播时间是通过第一，第二和第三类的椭圆形积分的组合给出的。对于卫星在空间分布的椭圆轨道上的更一般情况，传播时间由较高（第四）阶椭圆形积分表示，根据标准理论，可以通过低阶椭圆形积分反复表示。在具体情况下，第二和第四阶的椭圆积分通过非理性函数的组合和legendre形式的零级椭圆积分表示。已经证明，对于研究的情况，二阶椭圆积分可以通过基本功能表示。
The propagation time of a signal, emitted by a moving along an elliptical orbit satellite from the GPS (or GLONASS) satellite confi gurations is a very important ingredient of the theory, based on the formalism of the null cone and accounting for the effects of the General Relativity Theory. For the case of satellites, orbiting along a plane elliptic orbit, it has been proved that the propagation time for the signal between the satellites is given by a combination of elliptic integrals of the first, second and third kind. For the more general case of satellites on a space-distributed elliptic orbit, the propagation time is expressed by higher (fourth) order elliptic integrals, which according to the standard theory can be expressed recurrently by means of lower-order elliptic integrals. In the concrete case, the elliptic integrals of the second and the fourth order are expressed by means of a combination of irrational functions and the zero-order elliptic integral in the Legendre form. It has been proved that for the investigated case, second-order elliptic integrals can be expressed by elementary functions.
