Distance measurement with carrier phase

Carrier phase measurement is more complicated than code measurement. This is because the signal carrier phase don't have any time markers.

The principle of carrier phase measurement

Solving phase ambiguities, i.e. finding out how many whole wavelengths the distance between satellite and receiver consists of, is the critical part of carrier phase measurement.

The carrier phase on L1 has a much higher frequency than the C/A code, 1575 MHz, which corresponds to a wavelength of 19 centimetres. Based on the rule of thumb that the signal resolution is about one percent of the wavelength, an individual carrier measurement can in principle be made with an accuracy of about two millimetres!

Why does not all GNSS measurements use the carrier phase if it is so much more accurate than code measurement? The simple answer is that carrier phase measurement is more complicated, both in terms of equipment and method of measurement.

Illustration of the principle of carrier phase measurement. The satellite signal carrier phase and the GNSS receiver's copy of the signal can not be easily matched because the carrier phase is not time-stamped

The coded signal, such as the C/A code for GPS, is intentionally designed to facilitate signal matching and timing. However, the carrier phase has no time markers at all, because each full wavelength or period in the carrier phase is the same (see picture above; in reality the satellite signal is Doppler shifted, though).

Determination of integer phase ambiguities

The distance between satellite and receiver can in principle be expressed as a number of whole periods plus part of period (see picture below). the part of a period is carefully determined by phase measurement, but the number of whole periods will initially be unknown. ambiguity in English.This number is called phase ambiguity. The determination of phase ambiguities is therefore very critical for accurate positioning. If the integer phase ambiguity is wrongly determined, the measured distance between satellite and receiver ill be 19 centimetres too long or too short!

Illustration of the term phase ambiguity, which is the number of whole wavelengths of the carrier phase between satellite and GNSS receiver, when the measurement begins.

The determination of integer phase ambiguities is facilitated by

  • relative positioning, which reduces sources of error
  • multi-frequency measurement
  • good mathematical models
  • combination with code measurement, which provides the opportunity to limit or "circle" the number of possible integer phase ambiguities.

During real-time measurements, you want to combine these factors in different ways to minimize the time from the start of measurement to a so-called fixed solution, which means that the integer phase ambiguity has been determined ("fixed").This process is called initialization and requires the GNSS receiver to keep the satellite signal locked from the start of the phase measurement. Temporary interruptions result in an unknown number of periods being lost in the measurement, so-called cycle slips. If it is not possible to correct the cycle slips with an appropriate method, the phase measurement must be restarted.

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