Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates |
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Authors: | Yanming Feng Jun Wang |
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Institution: | (1) Department of Spatial Sciences, Curtin University of Technology, Perth, Australia; |
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Abstract: | The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed
to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has
been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for
the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and
computational load of the integration of the multivariate probability density function. Contributions of this work are twofold.
First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid,
at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available
in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily
obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding
and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates
obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS
AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed
with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that
variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates
from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions. |
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