## 7 Conclusions and Summary  
Evidence presented in this article indicates that despite the progress and increasing popularity, GNSS monitoring of bridges has some limitations, especially for short, stiff bridges, in which the SNR of geodetic estimates of deflections is low, even SNR \(<1\). In such cases, GNSS results may lead to excessive apparent semi-static and dynamic deflections of bridges, inconsistent with their overall performance. This is reflected in the contrast between evidence summarized in Tables 1 and 3. Table 1 indicates that the vertical dynamic deflections of stiff bridges are typically of sub-cm level; a result consistent with various Codes which predict maximum deflections of the order of up to a few cm to satisfy typical serviceability criteria (e.g., AASHTO [9]). Table 1 also indicates that deflections of the order of 20 cm are observed only during destructive tests of stiff bridges. Table 3 on the contrary, deriving from a careful study, indicate deflections of tens of centimeters for a concrete bridge with a span of 20 m and with no visual signs of damage, cracks, etc., and with no sense of discomfort because of high oscillations to passing vehicles. Quasi-similar results have been reported for other stiff bridges as well, but the study of [PERSON] et al. [30] is unique because it was made carefully, and because the authors were surprised by their results, for which they could find no explanation other than an unusual structural behavior. Hence the focus of the article was to find an explanation for this problem and propose ways to avoid it. Systematic field studies and experiments summarized in this study indicate that the source of error for amplified (and perhaps also attenuated) dynamic bridge deflections is a near-field effect, an impact of vehicles with large reflecting surfaces passing close to the antenna. These vehicles influence the received signal in two ways. First, the signal of certain satellites is reflected on passing vehicles before it arrives the GNSS antenna, and this additional distance (multipath), large for the wavelength of a radio signal, produces a bias in the instantaneous coordinates of the antenna and of the computed bridge deflections (see Figures 2b and 5). This represents a dynamic multipath effect, due to a rapidly moving reflecting surface near the antenna, correlating with traffic. Dynamic multipath is different from the quasi-static multipath deriving from reflections from static reflective surfaces, for example, bridge cables, corresponding to long-period noise because of the slow movement of satellites. Second, certain satellites may be instantaneously shadowed by passing vehicles (Figure 5), and hence the observations system (i.e., the set of satellites the signal of which is recorded by the antenna and analyzed) is instantaneously (temporarily) modified; this leads to instantaneous, spurious shifts of the antenna coordinates and to biased antenna (and bridge) deflections. The main characteristic of these two effects is a high-frequency impact on the instantaneous antenna coordinates and spurious bridge deflections, correlating with intervals during which vehicle with high reflective surfaces (and hence mass) passes next to the antenna. This gives the wrong impression of a causative relationship between high bridge loadings by lorries and high bridge deflections. Since no specific sensors to control bridge loading usually exist (e.g., [37]), certain simple techniques to avoid these types of bias in dynamic deflections (using the pattern of Figure 5) and recognize, even minimized them, were summarized in Section 6. However, once high-frequency deflections of a stiff bridge are contaminated by dynamic multipath, no healing is possible (cf. [16; 28]). This double, high-frequency bias can also be recognized in longer, flexible bridges (Figure 2b).