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Today in GPS navigation, an accuracy from 5 to 10 m can be achieved, but performance can be strongly degraded in a multipath environment. Multipath can introduce large errors when measuring the distance between the satellites and the GPS receiver. They are commonly modeled by additive-measurement noise variance jumps affecting GPS measurements if there is a direct path between the satellites and the receiver and by additive-measurement noise mean-value jumps otherwise. If two signals from satellites have close directions of arrival, they are very likely to be simultaneously degraded by multipath. Therefore, in this letter we suggest taking into account the spatial dependencies between GPS measurements when modeling multipath occurrence/disappearance. For that purpose, we use a probabilistic tool, namely copulas. Then, as the proposed model is strongly nonlinear and non-Gaussian, we jointly estimate the mobile location and perform the multipath detection/estimation by using particle filtering.