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Multipaths cause major impairments to navigation with the Global Positioning System (GPS). Indeed, non-line-of-sight (NLOS) propagation is well known to bias GPS position estimates. A recent methodology has been proposed to overcome this limitation by estimating simultaneously the kinematic states and the multipath biases all along the observation interval. However, multipaths clearly occur relatively infrequently during time intervals of fixed duration. The paper studies a particle filtering algorithm for joint detection and estimation of multipath biases. A Rao-Blackwellized approach allows estimation of the kinematic states by extended Kalman filters, whereas multipath detection is achieved by an appropriate fixed lag particle filter.