In urban canyons, non-line-of-sight (NLOS) multipath interferences affect position estimation based on global navigation satellite systems (GNSS). This paper proposes to model the effects of NLOS multipath interferences as mean value jumps contaminating the GNSS pseudo-range measurements. The marginalized likelihood ratio test (MLRT) is then investigated to detect, identify and estimate the corresponding NLOS multipath biases. However, the MLRT test statistics is difficult to compute. In this work, we consider a Monte Carlo integration technique based on bias magnitude sampling. Jensen's inequal- ity allows this Monte Carlo integration to be simplified. The multiple model algorithm is also used to update the prior information for each bias magnitude sample. Some strategies are designed for estimating and correcting the NLOS multipath biases. In order to demonstrate the performance of the MLRT, experiments allowing several localization methods to be compared are performed. Finally, results from a measurement campaign conducted in an urban canyon are presented in order to evaluate the performance of the proposed algorithm in a representative environment.