The Error Distribution and GDOP in GPS

Abstract

It is proved that the bivariate distribution of the positioning error in GPS can be estimated by the covariant matrix deduced from the allocation of satellites. A covariant ellipsis of equi-probability contour is drawn by standard deviations and covariance of one hundred horizontal positions fixed by a receiver, acquired continuously at every 5 seconds for about 8 minutes. It is then compared with the ellipsis by the covariance matrix deduced from the allocation of satellites at the mid-time of the acquisition. The comparison of 153 samples, observed at Tokyo, of the satellites combinations of 03-06-13, 03-06-09, 06-09-12 and 03-12-13 from March 9th to March 17th '88 confirms reasonably the coincidence of the two ellipses, although small discrepancies, which seem to be depending on the allocation and the combination of the satellites, are observed. Thus the reliable direction of positioning can be predicted by the allocation of satellites, even under the high GDOP allocation.