Variance components analysis of residual errors remaining in the GPS double-difference phase observations is presented in this paper. These errors arise due to unmodeled ionospheric,
tropospheric and multipath effects and limit the accuracy of n (northwards), e (eastwards) and u (upwards) coordinate estimates. In addition, there are unavoidable pure random errors. An integral approach to variance components estimation of the residual errors is presented herein. The mathematical basis of the approach lies in the two-way nested classification, where one uses a linear model with random effects. It turned out that, for a baseline of 40km in length at mid-latitude region and during a year of the lowest sunspot activity in the 11-year cycle, daily standard deviations estimates of combined tropospheric and ionospheric effects are with intervals of ~1–11mm, ~1–7mm and ~4–51mm for n, e and u coordinate, respectively. In the same order, for the multipath effects, the intervals are ~4–12mm, ~3–9mm and ~8–30mm, while with pure random error those are ~5–9mm, ~4–7mm and ~9–20mm. It is important to say that the highest values arise in summer and the lowest in winter period.

Key words: residual effects in GPS observations, two-way nested classification, variance components estimation, integral approach, directions for further research