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2.1无线电导航原理
无线电导航技术随着其他无线电应用技术的进步而进步。无线电导航系统的工作原理基于两个基本假设，即无线电波的传播机制是已知的并且无线电波的传播速度非常接近自由空间中的光速。另外，系统具有足够的带宽用于确定用户的位置、速度、高度信息。最后，所有的测量，如寻向、测量时延、相位和多普勒测量至少在用户端必须有低成本的技术实现方式。
早期的无线电导航系统使用发射或者接收天线的指向性。这些系统的主要误差来源于天线。由于其角度和位置误差都随着距离线性增长，严重的制约了作用范围和精度。因此仅用于将单个用户导向单个点，如将飞机导向跑道起点的ILS设备。
时间或者频率是能够最精确测量的物理量。如果传播速度和模式是已知的，我们很容易由时延计算出距离。此外除非考虑速度的不确定性，否则绝对测量精度和待测距离的数量级是无关的。因此所有长距离精确导航系统都基于时延测量或者时间微分，即多普勒测量。
最早的无线电测距方式是在待测地点安装应答机--发送信号并接受应答信号测量往返时间。尽管这种无线电导航系统曾经实用化过，但却有明显的缺点即需要发送和接收信号。这种系统无法适应用户数量不固定的状况，在一个时间点仅能有一人使用应答机并且测量还需要花费一定的时间。军事用途的用户往往不希望发送信号暴露自己的位置，民用用户也不希望导航设备需要申请许可。
如果用户可以实现并保持与导航发射机的同步，则用户端发送设备并不是必要的。例如用户和导航系统都装备高精度的时间/频率源如原子钟。这样用户可以将自己的时钟与已知地点的时钟同步，这样用户在任何地点都可以实现时延测量。
但是原子钟是昂贵、笨重、大功耗设备，我们需要提供一个更简单的方法给数量众多的仅具有被动接收端的用户。这样的系统需要大量的同步的发射器，见图。由于用户没有精确的时钟，不能直接测量时延得到d1,d2,d3。
用户仅可以测量发信器Tx的信号到达时差，这些时差对应着距离差。这些等距离差的点构成一条双曲线（二维）或旋转双曲面（三维）。发信器位于双曲线（面）的焦点。对于二维导航需要至少三个同步的发信器信号。如，Tx1和Tx2的时差信号可以得到d1-d2=常数的双曲线。同样的Tx2和Tx3的信号可以得到d2-d3=常数的双曲线。两条双曲线的交点就是用户的位置。
2.1. Radio-navigation principles
Radio navigation evolved together with other applications of radio waves. The operation of all radio-navigation systems is based on the assumption that the propagation mechanism of radio waves is well known and that the propagation speed of radio waves is usually very close to the speed of light in free space. Further, systems using radio waves usually have a sufficient range to be practically usable for position, velocity and attitude determination of a remotely-located user. Finally, all of the measurements on radio waves, like direction finding, time-delay measurements, phase measurements or Doppler-shift measurements, can be performed with simple and inexpensive technical means at least on the user side.
Early radio-navigation systems used the directional properties of the receiving antenna, transmitting antenna or both. In these systems the main sources of measurement errors are the inaccuracies of the antenna pattern(s). Since the measured quantity is an angle, the position error grows linearly with increasing the distance between the remote user at an unknown location and the navigation equipment at known location(s). Such systems are therefore severely limited in either the range or the accuracy and are only efficient to bring a user to a single point, like bringing an aircraft to the beginning of a landing runway using the Instrumented Landing System (ILS).
Time or frequency are certainly the physical quantities that can be measured most accurately. If the propagation speed and propagation mode of radio waves are known, one can easily compute the distance from a time-delay measurement. Further, the absolute accuracy of such distance measurements does not depend on the order of magnitude of the distances involved, except for the uncertainties in the propagation speed of the radio waves used. Therefore, all long-distance, precision radio-navigation systems are based on time-delay (or signal phase difference) measurements and/or the time derivatives of these quantities, usually observed as the Doppler frequency shift.
The easiest way to measure the distance to a known site is to install a radio repeater there, transmit a signal, receive the answer from the repeater and measure the round-trip time. Although such radio-navigation systems were practically implemented (like DME for civilian aircrafts), they have some limitations due to the fact that the user needs both to transmit and to receive radio signals. Such a system can not accomodate an unlimited number of users since only one user can use the radio repeater at a time and each measurement takes some time. Some military users may also not want to transmit any radio signals to avoid disclosing their position to the enemy while civilian users do not want the requirement of having their navigation equipment licensed.
The transmit requirement for the user can be dropped if the user can achieve and maintain synchronization with the navigation transmitters in a different way. For example, both the user and the navigation transmitters may be equipped with high-accuracy time/frequency sources like atomic clocks. The user then synchronizes his clock at a known location and the same clock is then used at an unknown location for time-delay measurements.
Since atomic clocks are expensive, bulky and power-hungry devices, a more simple alternative is desired for navigation systems serving a large number of passive, receive-only users. Such a system must have a number of synchronized transmitters as shown on Fig.01. Since the user does not know the accurate time, he can not measure the time delays and the distances d1, d2, d3... to the transmitters TX1, TX2, TX3... directly.
The user can only measure the differences in the times-of-arrival of different TX signals. Time differences correspond to distance differences. The set of points corresponding to a given distance difference from two given points is a hyperbola (in two dimensions) or a rotational hyperboloid (in three dimensions). The two transmitters are located in the focal points of the hyperbola (rotational hyperboloid).
For two-dimensional navigation (positioning) signals from at least three synchronized transmitters need to be received. For example, from the measured time difference between TX1 and TX2 the user can plot the hyperbola d1-d2=const.12 on his map. Similarly, from the measured time difference between TX2 and TX3 the user can plot the hyperbola d2-d3=const.23 on his map. The two hyperbolas intersect in a point corresponding to the unknown user location! |
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