ON THE SENSITIVITY OF THE LOCATION, SIZE AND SHAPE OF THE GPS AMBIGUITY SEARCH SPACE TO CERTAIN CHANGES IN THE STOCHASTIC-MODEL

In this contribution we analyse in a qualitative sense for the geometr y-free model the dependency of the location, the size and the shape of the ambiguity search space on different factors of the stochastic mod el. For this purpose a rather general stochastic model is used. It inc ludes time-correlation, cross-correlation, satellite elevation depende ncy and the use of an a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases . It is shown that the location is invariant for changes in the cofact or matrix of the phase observables. This also holds true for the cofac tor matrix of the code observables in the ionosphere-float case. As fo r time-correlation and satellite elevation dependency, it is shown tha t they only affect the size of the search space, but not its shape and orientation. It is also shown that the least-squares ambiguities, the ir variance matrix and its determinant, for, respectively, the ionosph ere-fixed model, the ionosphere-float model and the ionosphere-weighte d model, are all related through the same scalar weighted mean, the we ight of which is governed by the variance ratio of the ionospheric del ays and the code observables. A closed-form expression is given for th e area of the search space in which all contributing factors are easil y recognized. From it one can infer by how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplica tion factor is largest when one switches from the ionosphere-fixed mod el to the ionosphere-float model, in which case it is approximately eq ual to the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points inside the search space.