## 3 Bridge Type, SNR and Multipath in Geodetic Deflection Measurements
### The Threat of Dynamic Multipath  
Multipath is a threat for all radio-type waves, including those of GNSS. This problem arises from the fact that the signal from a satellite may not directly arrive at a GNSS antenna (in most cases combined with a receiver to form a compact GNSS unit; see Figure 2a), but it is first reflected to a certain surface, so that an increased distance between satellite and antenna is obtained. Figure 3: An example of denoising time series of GNSS-derived deflections of stiff bridges, in which the useful, high-frequency signal is masked by long-period noise. (**a**) Acceleration signal of the excitation of a certain bridge, stiff in the vertical axis. (**b**) the corresponding 100 Hz GNSS signal is covered by noise. (**c**) Band-pass filtering using structural constraints permits to reconstruct dynamic displacement. For details and analysis of a similar bridge excitation event, see [15]. Typical multipath represents a static or semi-static effect, because the satellite constellations above each site gradually change (satellite orbits are of the order of 24 h). In long bridges conventional multipath is usually produced by cables, producing secondary reflections to the signal arriving at a GNSS antenna. Specific types of antennas, like the one shown in Figure 2a (\"chock ring antenna\") reduce this effect. Exclusion of low-elevation satellites (i.e., adopting a \"mask angle\", i.e., an angle of 15\({}^{\circ}\), to exclude all satellites at an elevation smaller than 15\({}^{\circ}\), in analogy to astronomy) is another technique to suppress conventional multipath. Some computational techniques to mitigate multipath have also been proposed [27]. About 20 years ago, [PERSON] and [PERSON] [18], who introduced bridge monitoring using both GPS and RTS, noticed unrealistic apparent GPS-derived bridge deflections, of the order of about 10 cm (Figure 4) and assigned them to multipath (reflections of satellite signal to the nearby bridge cables. This noise, however, is a rather long-period effect (shifting of the base line at around 8:08 by about 10 cm). However, a closer look indicates an amplification of the RTS deflection signal in GPS data, and this represents a high-frequency effect. Corruption of the GNSS signal had been observed during the monitoring of a train bridge using both RTS and GNSS [16], and this inspired systematic studies of this type of noise. These studies included experiments with GNSS antennas on stable ground next to the train tracks, mimicking bridge monitoring. The results were surprising, for the satellite signal was corrupted during the passage of trains, and the peaks correlated with the number of wagons and their reflective surfaces; spurious peaks could even be used as time stamping for the passage of trains. Further analysis of this effect, indicated that the signal corruption derived from two effects [28], as is explained in Figure 5.  
Figure 4: One of the first cases of identification of corrupted GPS signal during the monitoring of a suspension bridge in Austria excited by traffic. Thin line indicates RTS measurements and deflections of about 2 cm; bold line indicates GPS measurements with characteristic type of noise: amplification of the deflection signal, and an about 10 cm offset, due to conventional (long period) multipath because of reflections of the slowly moving satellite signal to the bridge cables. First, shadowing of some satellites because of passing vehicles, so that the geometry of the observations system was _instantaneously_ changed, and this highly influenced computed coordinates and computed instantaneous deflections. In favorable cases, this effect may be treated in a simple way: temporarily shadowed satellites are excluded from processing of the whole time series of observations.