Measurement of deflections of certain bridges is usually hampered by corruption of the GPS signal by multipath associated with passing vehicles, resulting to unrealistically large apparent displacements. Field data from the Gorgopotamos train bridge in Greece and systematic experiments revealed that such bias is due to superimposition of two major effects, (i) changes in the geometry of satellites because of partial masking of certain satellites by the passing vehicles (this effect can be faced with solutions excluding satellites that get temporarily blocked by passing vehicles) and (ii) dynamic multipath caused from reflection of satellite signals on the passing trains, a high frequency multipath effect, different from the static multipath. Dynamic multipath seems to have rather irregular amplitude, depending on the geometry of measured satellites, but a typical pattern, mainly consisting of a baseline offset, wide base peaks correlating with the sequence of main reflective surfaces of the vehicles passing next to the antenna. In cases of limited corruption of GPS signal by dynamic multipath, corresponding to scale distortion of the short-period component of the GPS waveforms, we propose an algorithm which permits to reconstruct the waveform of bridge deflections using a weak fusion of GPS and RTS data, based on the complementary characteristics of the two instruments. By application of the proposed algorithm we managed to extract semi-static and dynamic displacements and oscillation frequencies of a historical railway bridge under train loading by using noisy GPS and RTS recordings. The combination of GPS and RTS is possible because these two sensors can be fully collocated and have complementary characteristics, with RTS and GPS focusing on the long- and short-period characteristics of the displacement, respectively.