Integer ambiguity validation: an open problem?

Abstract

The problem of integer estimation has drawn a lot of attention in the past decade, and is now often considered solved. However, a parameter resolution theory cannot be considered complete without rigorous measures for validating the parameter solution.In the classical theory of linear estimation, the variancecovariance matrices that come with the estimation provide sufficient information on the precision of the estimated parameters. This is because applying a linear model to normally distributed (Gaussian) data, provides linear estimators, which are also normally distributed. And we know that, in case of a multivariate normal distribution, the peakedness is completely captured by the variancecovariance matrix.Unfortunately, this classical theory does not apply to the integer GPS model because the estimators are not normally distributed anymore if the randomness of the integer estimators is taken into account. In practice, this randomness is often ignored, so that it is assumed that the classical testing theory can still be applied. Based on this assumption, several integer tests have been proposed in the past. Some of these tests give satisfying results and are widely used. However, it should be stressed that these tests are based on incorrect assumptions and lack a theoretical basis.This paper gives an overview of the existing methods of integer testing. These methods are compared and which tests give good results are investigated . Furthermore, the pitfalls inherited with these tests are discussed.

Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing

“…One possible reason for this could be that the observation weight matrix used in our processing was optimistic, because it ignored the correlations between the three observables. It should be pointed out however, that the typical validation tests are not rigorously defined and have high false rejection rates [25,26]. Therefore, for this paper, the usefulness of ambiguity resolution with PPP was determined by examining the actual positioning results obtained with the technique.…”

Triple-Frequency Code-Phase Combination Determination: A Comparison with the Hatch-Melbourne-Wübbena Combination Using BDS Signals

“…Even if, currently, the so-called "partial AR" strategy [42][43][44] arises to fix part of the ambiguities, how to select the subset of the ambiguity is another introduced problem. Additionally, for integer least-squares estimation, the procedure includes an integer ambiguity search and ambiguity validation, and the latter is a troublesome problem to be solved [45]. If sufficiently reliable, the integer rounding could be an alternative approach, and the selected optimal and suboptimal combinations in this paper make this possible.…”

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

“…Ambiguity validation for the test data was carried out by using the following discrimination tests: the ratio test (R-ratio, T R ) (Euler and Schaffrin, 1991), the F-ratio test (T F ) (Counselman and Abbot, 1989), and the difference test (D-test, T D ) (Tiberius and De Jonge, 1995). These tests work very well and provide the effective performance of validation, also when they are carried out without the acceptance test (Verhagen, 2004). Definitions of the tests are given by:…”