1.2.6 System Ingredients

MEASUREMENT TECHNOLOGY

Only those technologies based on microwave transmissions will be considered because:

• They can penetrate clouds and rain, and can operate day or night.
• They can be most readily implemented within the satellites themselves.
• They are similar to readily understood conventional (terrestrial-based) survey and navigation technologies, such as range and range-difference systems.

It is necessary to further distinguish between two-way and one-way ranging, and then to briefly introduce the measurement modes based on ranges and range-differences.

Two-Way and One-Way Ranging

Ranging by means of microwave signals can be done in either of two modes. Two-way ranging involves the measurement of the travel time of a signal by one clock. At one end of the line a device (for example, a glass prism, or microwave transponder) reflects the incoming signal back to the transmitter. The basic measurement is the travel time for the round trip distance. This is the procedure employed in several EDM and radio-navigation systems. Its major shortcoming however is that it is best suited for a single user system (the reflector-transmitter coupling required for a single measurement tends to be inflexible in a multi-user environment).

One-way ranging involves the measurement of the travel time of a signal from transmitter to receiver through the use of separate clocks. The transmitter clock generates the signal, while the receiver clock detects when the signal arrives. The difference in transmit and receive time is the travel or "transit" time, hence both clocks must keep the same time. (An error in synchronisation of the two clocks of 1 nanosecond is equivalent to 30cm in distance.) In general, each clock keeps its own time and the relationship between the clocks may have to be established from the measurements themselves. The main advantage of such a system is that it is "multi-user", each user being a passive "listener".

Figure 1. Two-Way and One-Way Ranging.

Range and Range-Difference Measurements

A range, or distance, measurement can be made to very high precision because it essentially involves the measurement of time delay, or signal transit time. Modern clocks are essentially frequency oscillators (section 1.3.1), perhaps based on a quartz crystal, or an atomic "clock" of some sort. Although each clock exhibits different stability characteristics (some are better for measuring long time intervals, others for short intervals), their overall stability is of the order of 1 part in 10¹⁰ to 10¹² (Table -- section 1.3.2). The distance is found by multiplying the time delay by the signal's speed of propagation (=299792458m/s in a vacuum). A time delay interval measured to this precision with a single clock translates to a distance precision of a centimetre or better. The use of two clocks, as in one-way ranging, complicates matters for a number of reasons:

The time delay measurement is affected not only by the quality of the clocks, but also on how well they are "synchronised". This itself is influenced by such factors as:

• how long since the last synchronisation (as the drift of the clocks since synchronisation is the issue, not the short term stability of the clocks for the time delay measurement),
• how well the synchronisation is carried out in the first place (seldom are the clocks able to be physically brought together and directly compared), and
• generally this is carried out by comparison with a third time scale, accessible to all clocks (including those in the orbiting satellites), and hence the quality of the definition and maintenance of this "master" time scale is an important issue as well.
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The "time-of-transmission" information must be made available to the second clock, and hence the resolution to which this information is available must be adequate (for example, if the digital time signal is defined by a frequency of 10MHz, then the resolution of time is 0.1 microsecond, or the equivalent of 30 metres in range!)

The former can be partly overcome by appropriate modelling of the biased range (section 1.3.3). The latter is important for instantaneous range measurements on GPS, but not for range measurements derived from carrier phase observations.

An alternative solution to both of these problems is to create range-differences. This is useful for measurements that contain timing (and other) errors that are linearly correlated, for example if the same bias affects both measurements, then differencing the two will eliminate that common bias. In the case of a single satellite-single station configuration, this approach aims to reduce the measurement to its simplest form, the measurement of a short time delay, so that rather than measuring a one-way range (with all the accompanying problems of synchronisation, etc.) between satellite and station, the change in transit time (or range) is what is important. Hence the exact time-of-transmission is not required, as the range-difference "measurement" is dependent only on the short term stability of both the station and satellite clock.

These "between-epoch" range-differences are the basis of the TRANSIT Doppler satellite measurement. These range-differences are inferred from the Doppler frequency shift. As a result of the TRANSIT satellite's movement, the frequency of the satellite signal changes continually. These frequency shifts, when integrated over a given time interval, are functionally related to the change in radial distance (or slant range, as it is sometimes known). The position of the receiver can be determined from these range-differences, as measured using one TRANSIT satellite.

Figure 2. The definition of range-difference.

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© Chris Rizos, SNAP-UNSW, 1999