8.1.4 GPS Baseline Processing

CARRIER-RANGE POSITIONING

To ap preciate the power of the "carrier-range" positioning solution it is necessary to rewrite eqn (7.2-4) to change the balance between known and unknown quantities in the double-differenced observation equation:

(8.1-1)

The quantities on the first line are known. The only unknown quantities are the coordinates of receiver 2. If the measurement noise is at the few millimetre level (no multipath and residual atmospheric biases are assumed to be present in the double-differences), then it would be possible to determine the three coordinate components of receiver 2 to centimetre level accuracy with just three independent double-differences (from the simultaneous tracking of four GPS satellites)!

Unambiguous carrier phase (or "carrier-range") positioning has all the advantages of pseudo-range positioning, such as instantaneous single epoch results, but with unprecedented precision. The Figure below illustrates a series of repeated single epoch results (the "carrier-range" data was processed in the "kinematic" mode) for the length of a static baseline. Note that the baseline length variability is of the order of a centimetre (similarly for the other components). The following comments can be made:

• The signature in figure below is largely due to the impact of multipath on the phase observations -- the multipath effect on pseudo-range would be up to several orders of magnitude greater.
• A change in the constellation of satellites from one epoch to the next will cause a "jump" in the solution.
• As the baseline was static, the redundant measurements are not contributing to the solution (solutions are carried out on a single epoch basis) -- redundant observations increase precision according to the "averaging law" ().
• The precision is influenced by the instantaneous satellite geometry as represented by navigation DOPs such as PDOP -- this varies smoothly over time except when satellites set below the tracking horizon or new satellites rise above it.
• For each epoch the repeated baseline estimates are derived from double-differenced precise "carrier-range" observations (eqn (8.1-1) as long as the ambiguities used in the previous epoch remain valid -- hence GPS hardware must continue to track the satellites (new satellites require new ambiguities to be estimated) and cycle slips must be avoided.

Single epoch baseline length solutions for a static baseline using carrier phase data with resolved ambiguities.

Some of the issues that must be addressed in order to make "carrier-range" positioning reliable are:

• How to prevent cycle slips?
  

  Requires new ambiguity resolution to be carried out, but how to do this quickly, reliably and without too great a nuisance to the surveyor?

   

• How to improve the precision of the solution and increase its "robustness"?

  
  

  Extra satellites, Kalman filter algorithms, dual-frequency observations, precise pseudo-range data, multipath resistant antennas and receiver electronics, etc.

   

• Is real-time "carrier-range" positioning possible, or desirable?

  It is possible for pseudo-range positioning. "Real-time kinematic" (RTK) is very attractive for many users, it would also help indicate to field staff if something goes wrong (loos of lock, etc.).

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