10.3.2  Carrier Phase Differential

The carrier phase measurement technique uses the difference between the carrier

phases measured at the reference receiver and user receiver.  A double differencing

technique is used to remove the satellite and receiver clock errors.  The first difference

is the difference between the phase measurements at the user receiver and the

reference receiver for a single satellite.  This eliminates the satellite clock error which is

common to both measurements.  This process is then repeated for a second satellite. 

A second difference is then formed by subtracting the first difference for the first

satellite from the first difference for the second satellite.  This eliminates both receiver

clock errors which are common to the first difference equations.  This process is

repeated for two other pairs of satellites resulting in three double differenced

measurements that can be solved for the difference between the reference station and

user receiver locations.  This is inherently a relative positioning technique, therefore

the user receiver must know the reference station location to determine its absolute

position.  Refer to Chapter 11 for a more detailed description of this process.

This same technique can be used to determine the attitude of a vehicle or platform.

 In this case the processing can be contained within one receiver using multiple

fixed antennas.  One antenna can be arbitrarily chosen as the "reference".  Since

the antennas are separated by fixed distances and since their relationship to the

center of mass of the platform is known, it is possible to convert the carrier phase

differences into angular differences between the antenna locations and the line of 

sight to a satellite.  By using measurements from multiple satellites, or the position

of the platform from a DGPS position fix, these angular differences can be

transformed to represent the attitude of the platform with respect to the local

vertical axis.

The "raw" phase measurements are essentially a count of the number of carrier

cycles between the satellite and receiver positions.  The number of cycles times the

carrier wavelength is a range measurement.  The receivers can directly measure

the fractional portion of the phase measurement and can track phase shifts

including whole cycles, but they must calculate the initial whole number of cycles

between the receiver and the satellite. This is referred to as the integer cycle

ambiguity.

For surveying applications, this integer ambiguity can be resolved by starting with

the mobile receiver antenna within a wavelength of the reference receiver antenna.

 Both receivers start with the same integer ambiguity, so the difference is zero and

drops out of the double difference equations.  Thereafter, the phase shift that the

mobile receiver observes (whole cycles) is the integer phase difference between

the two receivers.  For other applications where it is not practical to bring the

reference and mobile antennas together, the reference and mobile receivers can

solve for the ambiguities independently as part of an initialization process.  One

way is to place the mobile receiver at a surveyed location.  In this case the initial

difference is not necessarily zero but it is an easily calculated value.

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