8.3.5 Ambiguity Resolution: The Key to Modern GPS Surveying

TEST AND REJECTION CRITERIA FOR AMBIGUITY RESOLUTION

The st andard test criteria is based on the ratio of "best" RSS of the observation residuals to the "second best" (eqn (8.2-4)) . The correct ambiguity set is assumed to have been identified if the ratio is larger than some specified threshold value. A more formal approach is to define the test statistic and to then test this statistic against an expected value, at some confidence level. For example, the test statistic may be defined as (HAN & RIZOS, 1996):

(8.3-4)

where the aim of the test is to discriminate between the smallest RSS value ( m_s ) and any other RSS value ( m_i ). The rejection criteria for the ambiguity set corresponding to m_i being if:

(8.3-5)

where:

n	is the number of double-differenced observations,
t	is the number of estimated parameters,
Fn-t,n-t	is the F distribution with (n-t,n-t) degrees of freedom, and
Fn-1,n-1; 1-	is the boundary of the 1- confidence interval, where is usually taken as 5%.

All candidate ambiguity sets generate an RSS value m_i, and the aim of the test is to see if there is a "statistically significant" difference between any of these RSS values and the smallest RSS value. If after testing all the candidate ambiguity sets against the prime candidate set (the one generating the smallest RSS value) it is found that no other ambiguity set can be considered "statistically close" the prime candidate set (by all failing the test at eqn (8.3-4)), then the prime ambiguity set is indeed the correct set and the ambiguity resolution process has concluded successfully.

There are several comments to be made with regard to such ambiguity resolution tests:

• The definition of the test statistic (eqn (8.3-4)) can vary.
  
• Under conditions of short observation sessions, weak satellite-receiver geometry, the presence of multipath and other biases, the correct ambiguities may in fact not generate the smallest RSS value. In this case, it would be unfortunate if ambiguity resolution was unsuccessful (that is, there is an insignificant difference betw een the smallest and the second or third smallest RSS values), but disastrous if the ambiguity resolution process was thought to have concluded successfully and the false ambiguity set was selected!
  
• The sensitivity of the test is somewhat arbitrary as the aim is for the test to be sensitive enough to eliminate many of the bogus candidate ambiguity sets, but not too sensitive to cause a false ambiguity set to be selected as the correct one.
  
• The best procedure may be to incorporate a number of different tests (each with a different "power" for eliminating bogus ambiguity sets, but which do not reject the correct set), in a certain order as suggested by ABIDIN ( 1993, 1994) in his "integrated on-the-fly ambiguity resolution approach" -- see Figure below.

There is much R&D being carried out at present in this area.

Ambiguity resolution multiple testing procedure as suggested by ABIDIN (1993).

Despite the tremendous progress made in the development of ambiguity resolution algorithms in the past few years, it is important to keep in mind the inherent weaknesses of short observation session techniques, as ambiguity resolution under such circumstances is not a totally foolproof procedure: Increased multipath susceptibility, of both phase and pseudo-range data. Very susceptible to the quality of satellite-receiver geometry. Only applicable for short baselines, as baseline increases then observation session length must also increase in an attempt to overcome the increasing influence of residual biases. There is always the risk that not enough data is collected in the field to obtain an ambiguity-fixed solution when data is post-processed, resulting in degraded baseline accuracy. Real-time processing is therefore an attractive alternative. In the event that the ambiguities are incorrectly resolved it is the baseline linking the base and rover receiver that is degraded. If signal lock is maintained (such as when the "stop & go" technique is used), then the positions of visited rover sites relative to each other are correct. This factor may be useful for certain observational scenarios. An increased emphasis should be placed on survey planning as more complex logistics may be required, and in order to take advantage of the greater productivity of these techniques (section 5.5.1), and to ensure that good Quality Control practices are always followed (section 10.1.1 and section 10.3.6).

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© Chris Rizos, SNAP-UNSW, 1999