Integer carrier phase ambiguity resolution is the process of resolving unknown cycle ambiguities of doubledifferenced carrier phase data as integers, and it is a prerequisite for rapid and high-precision global navigation satellite system positioning and navigation. Besides integer estimation, integer ambiguity resolution also involves validation of the integer estimates. In this contribution a new ambiguity resolution method is presented, based on the class of integer aperture estimators, which for the first time reveals an overall approach to the combined problem of integer estimation and validation. Furthermore, it is shown how the different discrimination tests that are currently in use in practice can be cast into the framework of the new approach.
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.
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