A proper choice of the observation weight matrix is of importance for both adjusting and testing GPS data. Our understanding of the noise characteristics of GPS observations, on which the weight matrix should be based, is however still underdeveloped. This makes it difficult to draw up an appropriate weight matrix. The first and foremost purpose of this contribution is therefore to draw attention to the need to improve upon our rudimentary knowledge of the GPS stochastic model. To this end, results will be presented of a relatively simple casestudy in which the possible presence of cross-correlation between observables is considered. With these results we hope to spur further discussion and research on this important topic.