Vehicles such as passing trains produce significant short-term biases in coordinates of nearby GPS stations, preventing these coordinates from being used for structural monitoring of bridges. In order to study this problem, we carried out experiments with receivers recording at 100 Hz and located on both sides of a rail next to passing trains. The experiments focused on trains with similar characteristics and velocity. The analysis of the data revealed a short-duration bias in coordinates with amplitude up to 10 cm and high spectral frequencies. This bias is not due to wrong integer ambiguity fixing, software defects, and changing geometry of satellites and it does not significantly improve with the addition of GLONASS satellites. It is partly due to temporary blocking of certain satellites by passing vehicles and a dynamic multipath due to fast-moving, near-field reflective surfaces. This dynamic multipath seems to depend on the geometry of satellites and to be characterized by a shift of coordinates during the whole interval of the vehicle passage, as well as by very short-period coordinate fluctuations which are related to specific morphological characteristics of the train reflective surfaces. The amplitude of the dynamic multipath is smaller in the horizontal coordinates, which are also characterized by a clearer pattern than the vertical coordinates. On the basis of the above results, certain strategies for the modeling of the dynamic multipath are proposed.