自制GPS发射机系列之一 ——无线电导航2
本帖最后由 longyun 于 2010-1-16 16:28 编辑对于三维导航至少需要四个同步发射器的信号。三个独立的时间差得到三个旋转双曲面。两个曲面相交得到一条曲线，曲线与第三个曲面的交点既是用户的三维坐标。
如果有更多可用的发射机，用户可以选择其中最好的三个（四个）提供两条双曲线（三个双曲面）的交点。其他发射机可以提供误差信息因为曲线和曲面可能不只有一个交点。
双曲导航系统首先在陆基导航中得到应用，他们工作在中波或长波段，如LORAN、DECCA和OMEGA。因为发射台都在地球表面，所以做不到三维导航。这些系统可以得到可靠地经纬度。对于高度测量，需要一台发射机处于接收机地平面之上或者之下。
陆基无线电导航系统使用相对低的频段的无线电波以获得较大的接收范围和避免空间传播方式（电离层反射）。如OMEGA系统使用频率10-14kHz的无线电波，8个发射基站就实现了全球覆盖。
在计算机未实用化以前人们发明了长波导航系统：使用固定发射基站进行二维导航可以最大限度降低用户端的计算量。各基站间的双曲线族可以在地图中直接绘制出来，甚至包括不规则传播导致的误差修正。
人造地球卫星最早的一个用途就是之一就是导航。显然卫星本身就需要导航，以确定火箭的发射轨道和卫星最终定点轨道。另一方面是，外太空是放置导航发射机的理想场所，因为VHF（甚高频）很宽的一段频谱的无线电波都可以以可预测的方式传播，电离层的影响是很小的。另外由于发射机定点在空间轨道上地面的三维导航就可以实现。
因为最早卫星仅能发射到低轨道——第一代导航卫星发射到距地心约1000km的极地轨道，如美国的TRANSIT卫星和苏联的TSIKADA卫星。因为卫星在低轨道上快速移动，单个卫星就能实现位置测定。在分钟的时间尺度内，甚至最简单的石英晶振提供的时间都可认为是非常精确的，卫星在此时间尺度内位置显著移动等价于沿轨道有好几个不同的发射机。
使用时用户测量一段时间内卫星信号的多普勒频移，利用卫星轨道数据计算自己的位置。尽管一颗卫星就能满足定位的需求，系统通常仍然由6（TRANSIT）到12颗卫星组成，以扩大覆盖范围，因为对于低地轨道卫星在同一时刻仅部分用户可见。由于电离层多少对于VHF和UHF（超高频）电磁波传播有影响，所以不论美国还是苏联都在约150MHz和400MHz两个频道发射导航信号。确切频率比为3/8，发射机是相干的用来得到电离层修正。
近地轨道卫星导航系统的缺点是用户需要等待卫星通过其上空，甚至测量也需要花上几分钟的时间。另外用户的速度方向和大小必须已知用来补偿多普勒频移计算。为了实现实时测量，我们需要更多的卫星。如果用户有至少四颗可见的卫星，他就能实时计算三维坐标而不需要等待。
为了减少卫星需求数，就需要把卫星发射到更高的轨道。这就是美国的GPS和苏联的GLONASS系统，用24颗卫星实现全球覆盖。这两个系统在地球的任何地点都提供了至少4颗可见的卫星，并且分布合理以实现三维导航。
最后需要注意，卫星导航系统需要用户端完成大量计算任务。卫星的位置在不断变化，所以没有双曲线投影在地图上。三维导航的要求更高，所以数字计算机是必须的。这或许就是最近卫星定位才变得流行的原因：尽管导航卫星已有30年的历史，但是廉价的计算器却不然。 以下是原文
For three-dimensional navigation signals from at least four synchronized transmitters need to be received. The three independent time differences generate three different rotational hyperboloids. Rotational hyperboloids are curved surfaces. Two of them intersect in a curved line which in turn intersects with the third hyperboloid in a point corresponding to the unknown three-dimensional user position.
If there are more transmitters available, the user can select the best set of three (four) that provide two hyperbolas (three rotational hyperboloids) intersecting as close as possible under a right angle(s). The remaining transmitters can then be used to check for errors and/or ambiguous solutions, since with curved lines and surfaces there can be more than one intersection point.
Hyperbolic navigation systems were first implemented as ground-based navigation systems operating in the medium and long-wave radio frequency spectrum like LORAN, DECCA or OMEGA. Since the transmitters are located on the Earth's surface, the geometry of the problem does not allow a three-dimensional navigation. These systems only measure the longitude and latitude reliably. To measure the altitude, one of the transmitters should be located above or below the user's receiver or at least out of the user's horizon plane.
Ground-based radio-navigation systems use relatively low frequencies of the radio spectrum to achieve a large radio range and avoid undefined skywave (ionospheric) propagation at the same time. For example, OMEGA uses the frequency range between 10 and 14kHz to achieve world-wide coverage with just 8 (eight) transmitters!
Long-wave radio-navigation systems were designed when digital computers were not readily available yet: two-dimensional navigation with fixed transmitter sites only requires a minimum of computations to be performed by the user. The families of hyperbolas for each transmitter pair can be directly plotted on maps, including corrections for known propagation anomalies.
One of the first applications of artificial satellites was radio navigation. Obviously artificial satellites need radio navigation themselves, to evaluate the performance of the rocket carrier and determine the final satellite's orbit. On the other hand, the space environment is an ideal place for navigation transmitters, since a large radio range can be achieved at VHF and higher frequencies where the propagation of radio waves is predictable and the influence of the always-changing ionosphere is marginal. Finally, the location of navigation transmitters in space can be chosen so that three-dimensional navigation is possible everywhere on the Earth's surface.
Since initially the satellites could only be launched in low-earth orbits, the first navigation satellites were launched in low, 1000km altitude, polar orbits, like the American TRANSIT satellites or the soviet equivalent TSIKADA. Since a satellite in a low-Earth orbit is quickly moving along its orbital track, a single satellite may be used for position determination. While even a simple crystal-controlled user's clock is sufficiently accurate for a few minutes, the satellite significantly changes its position on the sky and this is roughly equivalent to several navigation transmitters at several different sites along the orbital track.
In practice the user simply measures the Doppler shift on the satellite's signal for a certain period of time and computes his unknown position from the result of this measurement and the satellite's orbital data. Although a single satellite is required for position determination, these systems usually have from six (TRANSIT) up to twelve satellites to improve the coverage, since a low-Earth orbit satellite is only visible for a limited amount of time for a user located on the Earth's surface. Since the ionosphere still has some effect on VHF and UHF radio waves, both American and Soviet satellites transmit on two frequencies around 150MHz and around 400MHz. The actual channel frequencies are kept in the precise ratio 3/8 and the transmitters are kept coherent to allow for ionospheric corrections.
The drawbacks of low-Earth orbit navigation satellites are that the user may have to wait for a satellite pass and even then the measurement takes several minutes. Finally, the user velocity, both magnitude and direction, must be known and compensated-for in the position computation. To allow an almost instantaneous position determination more satellites are required. If a user has at least four visible satellites in different parts of the sky, he can compute his three-dimensional position instantaneously, without having to wait for the satellites to move across the sky.
In order to limit the number of satellites required, these have to be launched to higher orbits. Such satellite navigation systems are the American GPS and the soviet GLONASS that should achieve world-wide coverage with 24 satellites each when completed. Both systems should provide at least four visible satellites in any part of the world including in-orbit spares and a suitable distribution of the visible satellites on the sky to allow a three-dimensional navigation.
Finally, one should notice that satellite navigation systems require a large amount of computations to be performed by the user. The satellites continuously change their positions, so no hyperbolas could be plotted on maps. Three-dimensional navigation is even more demanding, so that a digital computer is absolutely necessary. Maybe this explains why satellite positioning only became popular a few years ago: although navigation satellites were available for more than 30 years, inexpensive computers were not! 基本介绍部分结束了，下一次将翻译关于星载系统以及有关GPS信号编码方面的内容。关于卫星轨道和大地测量方面我不是太关心，有兴趣可以看看原文。
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