8.1.5 GPS Baseline Processing

AMBIGUITY RESOLUTION

What is ambiguity resolution? The mathematical process of converting ambiguous ranges (integrated carrier phase) to unambiguous ranges of millimetre measurement precision ... For conventional GPS surveying, corresponds to converting real-valued ambiguity parameter values to the likeliest integer values ...

As has been emphasised several times, if the carrier beat phase observations were not "accumulated" or "integrated", by measuring the change-in-phase, or range, from the epoch of initial signal lock-on, the value on n would change with each epoch. This would make carrier phase observations all but useless. Hence determining the value of this unknown initial (integer) ambiguity is an important task of GPS data reduction software.

In an ambiguity-free solution, no advantage is taken of the integer nature of n as it is indistinguishable from other, non-integer, biases such as orbit uncertainties, multipath and atmospheric refraction (ionosphere and troposphere), and is in fact "contaminated" by them. Thus, "ambiguity resolution" as it is generally known, is only possible after all biases are eliminated or otherwise accounted for to better than one cycle (20cm wavelength on L1). Constraint of an ambiguity value to its correct integer will improve the estimation of the remaining geodetic (station coordinate) parameters, as an inspection of figure below indicates.

The Figure below illustrates what happens in a sequential transition from an 100% ambiguity-free solution to an 100% ambiguity-fixed solution. For the first ten epochs the solution is an ambiguity-free one, but after 10-15 epochs, when the ambiguities have been resolved, the precision of the remaining estimable coordinate parameters improves significantly. It should be noted that the precisions (as well as the numeric values of the parameters) have virtually converged to their final values immediately after all ambiguities have been resolved. As a corollary therefore, phase data collected beyond the minimum necessary to ensure an ambiguity-fixed solution is obtained has almost no influence on the final results.

Considerable R& D effort has been invested in so-called "rapid ambiguity resolution" algorithms, which are the basis of the "rapid static" GPS surveying techniques (section 5.5.2 and section 8.3.1).

The change in quality of baseline components in an ambiguity-free compared to an ambiguity-fixed solution.

Clearly, an ambiguity-fixed solution is very desirable, and all efforts should be made to obtain one. There are several steps involved in obtaining an ambiguity-fixed solution:

• Define the apriori values of the ambiguity parameters.
• Use a search algorithm to identify likely integer values.
• Employ a decision-making algorithm to select the "best" set of integer values.
• Apply ambiguities to the new (ambiguity-fixed) solution.

Ambiguity resolution is discussed in detail in section 8.2.1 and section 8.3.1. Although ambiguity resolution can be considered largely an optional solution strategy for conventional (static) GPS surveying, it is a vital operation for some of the modern high productivity GPS surveying techniques.

Maximising the Chances of Successful Ambiguity Resolution

There are some well-known strategies that can be employed for maximising the chances of resolving ambiguities (though it cannot be guaranteed) for conventional static GPS surveying, including:

• Single frequency observations for short baselines ( < 20km ).
• Dual-frequency observations for longer baselines.
• Adequate length observation session ( 1/2 hour --> 2 hours ).
• Minimise interference (for example, no multipath, low unmodelled ionosphere, etc.), by good selection of sites, observing at night, etc.
• Observe as many satellites as possible to ensure good receiver-satellite geometry.
• Use precise pseudo-range data if available (and the ambiguity resolution algorithm can make use of this data -- see sections 8.2, 8.3 and 8.4).

Factors making ambiguity resolution difficult include (section 8.2.4):

• The degree to which the geodetic parameters are reliably separated from the ambiguity parameters.
• The magnitude of any unmodelled biases present in the double-differenced phase data.
• The length of the baseline.
• The quality of the receiver-satellite geometry, and how much it has changed during the observation session.
• The data quality.
• Sub-optimal algorithms.

RELIABLE ambiguity resolution is essential ... Incorrect resolution of some ambiguities will lead to a poor solution (worse than ambiguity-free or triple-difference solution). Hint: has the solution changed by more than 10cm? How does one know when Ambiguity Resolution is possible? IT IS NOT POSSIBLE to be certain!! but with 1hour sessions to > 4 satellites; baselines < 20km & rapidly changing pdop it should be possible to resolve ambiguities.

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