This paper proposes a novel positioning technique suitable for use in mobile robots in urban environments in which large global navigation satellite system (GNSS) positioning errors occur because of multipath signals. During GNSS positioning, the GNSS satellites that are obstructed by buildings emit reflection and diffraction signals, which are called non-line-of-sight (NLOS) multipath signals. These multipath signals cause major positioning errors. The key concept considered in this paper is the estimation of a user's position using the likelihood of the position hypotheses computed from the GNSS pseudoranges, consisting only of LOS signals based on the analysis of the pseudorange residuals. To determine the NLOS GNSS signals from the pseudorange residuals at the user's position, it is necessary to accurately determine the position before the computation of the pseudorange residuals. This problem is solved using a particle filter. We propose a likelihood estimation method using the Mahalanobis distance between the hypotheses of the user's position computed from only the LOS pseudoranges and the particles. To confirm the effectiveness of the proposed technique, a positioning test was performed in a real-world urban environment. The results demonstrated that the proposed method is effective for accurately estimating the user's position in urban canyons.