CARRIER PHASE MEASUREMENTS |
The wavelengths of the carrier waves are very short -- approximately
19cm for L1 and 24cm for L2 -- compared to the C/A and P code chip lengths.
Assuming a measurement resolution of 1-2% of the wavelength, this means
that carrier phase can be measured to millimetre precision compared
with a few metres for C/A code measurements (and several decimetres for
P code measurements). Unfortunately, a phase measurement is "ambiguous"
as it cannot discriminate one (either L1 or L2) wavelength from another.
In other words, time-of-transmission information for the L-band signal cannot
be imprinted onto the carrier wave as is done using PRN codes (this would
be possible only if the PRN code frequency was the same as the carrier wave,
rather than 154 or 120 times lower in the case of the P code, and 1540 or
1200 times lower for the C/A code). The basic phase measurement is therefore
in the range 0° to 360° (see Figure 1 below). It is nevertheless
the basis for GPS surveying, and high precision kinematic positioning.
Figure 1. Carrier phase measurements.
There are essentially two means by which the carrier wave can be recovered from the incoming modulated signal:
Reconstruct the carrier wave by removing
the ranging code and broadcast message modulations.
Squaring, or otherwise processing the received
signal without using a knowledge of the ranging codes.
In the first technique the ranging codes (C/A and/or P code) must be known. The extraction of the Navigation Message can then be easily performed by reversing the process by which the bi-phase shift key modulation was carried out in the satellite. In the latter method no knowledge of the ranging codes is required. More complex signal processing is required to make carrier phase measurements on the L2 signal under conditions of Anti-Spoofing.
Integrated Carrier Beat Phase
Raw carrier phase measurements are generally the by-product of all GPS receivers.
These phase measurements cannot be used as "range" observations
because they are ambiguous, and furthermore, the ambiguity changes continuously.
The ambiguity is therefore a function of both the receiver channel tracking
the satellite, and time. (This is analogous to making terrestrial distance
measurements using only the "reader" portion of a steel band.)
It is very difficult to resolve the continuously changing unknown ambiguity
in a navigation solution (as can be done in the case of the receiver clock
bias).
But all is not lost! If it were possible to keep track of the number of whole wavelengths of the carrier wave as it is sampled within, for example, a phase-lock loop, then the integrated carrier phase observation could be generated:
 |
(3.2-1) |
where 
ji is the fractional phase (measured
as an angle in the range 0° to 360°, where 360° corresponds
to about 19cm for the L1 phase and 24cm for the L2 phase, see Figure
2), and CR is the current reading on a zero-crossing "counter",
that only registers the number of whole cycles since lock-on when the counter
had an initial value of CRo (usually zero). The term in square
brackets is therefore an integer. The additional electronics to
count the whole cycles since lock-on is the identifying characteristic of
GPS "surveying" receivers.
The relationship between ji(Tj)
and the range 
ji (Tj) is:
 |
(3.2-2) |
where nji is the ambiguity term, and v contains all the biases and errors affecting this measurement (section 6.2.1). (f0 / c) scales range into units of cycles. Note that nji is assumed to be constant over time, for a particular receiver-satellite combination, as illustrated in figure above. In order to convert this phase observation into range, the cycle ambiguity has to be determined. If the integer nji can be correctly determined, then the resulting "phase-range" (or "carrier-range") will be a very precise range (at the level of a few millimetres).
Figure 2. Integrated carrier phase and the ambiguity term.
Extraction of Carrier Beat Phase: Reconstructing the Carrier Wave
This is the technique used within code-correlating
receivers. When the spread spectrum signal is received at the
GPS antenna, the signal power is below the background noise (Figure 3 below).
After the ranging code modulations are removed by the procedure described
above, the satellite signal collapses into the original very narrow carrier
frequency band and signal power is again boosted well above the background
noise.
Figure 3. Spreading and de-spreading the spectrum of the carrier wave. (After
NATO, 1991)
By mixing a locally generated sine wave at the same frequency as the "reconstructed" received carrier (modulated only by the Navigation Message), the broadcast message can be extracted. The incoming and receiver-generated sine waves are continuously aligned within a "phase-lock loop" (section 4.1.3). Periodic sampling of the phase of the local carrier provides the carrier beat phase observable (Figures 3 above and Figure 4 below), which although useful for some applications such as the "phase smoothing" of pseudo-ranges, is still not suitable for survey applications. A much more useful carrier phase observable can be constructed through the "integration" of carrier phase measurements (see below).
Measurement of carrier beat phase on L2 by this technique requires a
knowledge of the P code generating algorithm. Under the policy of Anti-Spoofing,
the Y code is secret and hence cannot be used in this code-correlating mode.
The easiest option for GPS instrument manufacturers is to use the "squaring"
technique (or some variation of it) to make L2 phase measurements. However,
the primary advantage of the code-correlating approach is that it
results in a far better signal-to-noise ratio, and hence better quality
measurements, than any other signal processing technique.
Figure 4. Reconstructing the carrier wave and extraction of pseudo-range
data.
Extraction of Carrier Beat Phase: "Squaring" the Carrier Wave
In principle, the operation of a squaring receiver is very simple. The incoming signal is first converted to an intermediate frequency (IF) signal. The carrier, or rather the beat frequency carrier wave, is obtained simply by squaring this signal. Any phase inversions in the IF signal due to the PRN codes or message are removed. (This happens because a phase inversion is a change in the IF signal amplitude from "+1" to "-1", or from "-1" to "+1", and the instantaneous amplitude is either "+1" or "-1". Squaring the signal results in a signal with constant amplitude of unity, and hence the codes and message information are lost.) However, squaring the signal also squares the noise.
Aside from resulting in a noisier measurement, the squared carrier wave measurement is made on a carrier wave of double frequency. That is, the effective wavelength is of the order of 9.5cm on L1 and 12cm on L2. Figure 5 below illustrates this measurement scheme.
 |
 |
Figure 5. Extracting carrier phase from incoming GPS signals by carrier wave squaring.
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© Chris Rizos, SNAP-UNSW, 1999