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In Global Navigation Satellite System (GNSS) positioning, some unmodeled errors critically affect the accuracy and reliability of positioning solutions. When the unmodeled errors are significant in the mathematical model, they are mainly processed by choosing the adjustment models with additional systematic error parameters or semiparametric estimation. However, many existing methods tend to require knowledge of the prior information of unmodeled errors; otherwise, achieving better processing results is difficult. To address this problem, this paper proposes a GNSS unmodeled error separation method that does not rely on prior information of unmodeled errors. This method is built based on the constraint of the prior variance of unit weight. To begin with, the method effectively separates the effect of unmodeled errors in the residuals under this constraint. Secondly, the initial estimate of unmodeled errors in the observation domain is used as a virtual observation. Thus, the optimal estimate and variance of unmodeled errors are obtained. Finally, the observations are effectively corrected by combining the ideas of mean shift and variance inflation. In this paper, multiple sets of experiments are conducted. The results show that the proposed method can effectively weaken the impact of unmodeled errors on the float and fixed solutions of GNSS positioning, whether the unmodeled errors exist in a single observation or multiple observations.