In urban canyons, non-line-of-sight (NLOS) multipath interferences affect position estimation based on Global Navigation Satellite Systems (GNSS). In this paper, the effects of NLOS multipath interferences are modeled as mean value jumps appearing on the GNSS pseudo-range measurements. The Marginalized Likelihood Ratio Test (MLRT) is proposed to detect, identify and estimate the NLOS multipath biases. However, the MLRT test statistics is generally difficult to compute. In this work, we consider a Monte Carlo integration technique based on bias magnitude sampling. The Jensen inequality allows this Monte Carlo integration to be simplified. The interacting multiple model algorithm is also used to update the prior information for each bias magnitude sample. Finally, some strategies are designed for estimating and correcting the NLOS multipath biases. Simulation results show that the proposed approach can effectively improve the positioning accuracy in the presence of NLOS multipath interferences.