Considering Variances of Quasi-Random Effects in Relative GPS Positioning Performed During Daytime and Nighttime Periods – A Novel Two-Stage Approach

Abstract

In this paper, a new two-stage approach, involving an integral treatement of all quasi-random effects limiting the accuracy of relative GPS positioning and the method of moments to obtain final variance components regarding the effects of short-term (“far-field”) multipath (factor b), joint action of long-term (“near-field”) multipath and receiver antenna phase center offset and variations (factor a1), as well as joint action of tropospheric and ionospheric refraction (factor a2), is presented. In the study, GPS data collected on five baselines were used. Variance components of the quasirandom effects were obtained for the three relative GPS coordinates (e, n and u) using individually monthly datsets including daytime- and those including nighttime-wise ambiguity-fixed baseline solutions. The related results show that statistically significant inequality exists when comparing corresponding variances obtained for daytime and nighttime periods. It turned out that the following standard deviation estimates intervals are present (by the coordinates e, n and u, respectively): (a) daytime period: 3.3–6.9, 4.6–9.0 and 9.1–20.3 mm (factor b); 1.5–4.7, 1.9–7.0 and 3.4–21.9 mm (factor 1a ); 0.0116– 0.3282, 0.0103–0.2365 and 0.1222–0.7818 mm/km (factor a2); (b) nighttime period: 3.2–4.9, 4.7–7.3 and 8.4–15.4 mm (factor b); 0.8–3.8, 2.1–5.0 and 3.1–15.8 mm (factor a1); 0.0118–0.2734, 0.0097–0.2289 and 0.0752–0.6315 mm/km (factor a2).