## 4 Experimental Results  
Figure 13 shows a photo of the Weitinger Neckartal Bridge on Highway 81 from Stuttgart to Singen. The bridge is 900 m long and around 127 m above ground at its highest point. The bridge is made of five spans, and its two end spans consist of inverted cable stay towers that support massive beam spans of 263 m on the southern side and 234 m on the northern side. The bridge has four lanes, two for each driving direction. The total width of the bridge deck is 31.5 m.  
Figure 14 shows the schematic of the Neckartal Bridge indicating the deployed GNSS receiver nodes together with the two relay nodes and the GSM base station. Three GNSS receivers were placed on the deck of the bridge, one above the first pillar (Node E2), one just in the middle of the span between Pillars 1 and 2 (Node E3) and one in the middle of the bridge (Node E4). A GNSS reference node (E1) was placed on the ground before the bridge. As the distances from E1 and E4 to the base station were quite large, they only logged the data. Due to the strong attenuation of the radio waves by the steel girder box, the data could not be sent directly from the bridge deck to the GSM node located inside the steel girder box. Therefore, the data were sent from the GNSS sensor node to a relay node located below the deck on top of one pillar, as shown in Figure 15b. Figure 15a exemplary shows a GNSS receiver antenna attached to the bridge by magnets. It can be seen that the antennas have a unobstructed view of the horizon. Figure 14: Deployment of the wireless sensor network consisting of three rover nodes, a reference node, two relay nodes and the GSM base station. Figure 13: Photo of the Neckar Valley bridge near Weitingen in southwest Germany. The above-described points E1, E2, E3 and E4 have been installed with GNSS equipment and measured for a period of 40 min. Then positions E2 and E3 were logging and sending data for four consecutive days applying a logging period of three times 30 min per day. For reasons of clarity, the following processing examples are showing selected samples of 10 min for each of the mentioned points taken from the first 40 min interval. At first, the GNSS raw data are processed by applying the software RTKLib [44] developed by [PERSON] and [PERSON] at the Laboratory of Satellite Navigation, Tokyo University of Marine Science and Technology, Japan. The RTKLib offers a sophisticated post-processing module, RTKPOST, that applies ambiguity fixing strategies, to achieve the required accuracy for structural monitoring. Depending on the distance between the GNSS base station and the rover point, accuracies in the region of one to five millimeters are possible. To eliminate the main error sources of GNSS position, this package applies double differencing as introduced above in Section 3.2 within an extended Kalman filter. A detailed description of the applied algorithms may be found in [44]. The resulting point positions from GNSS processing are usually represented as Earth-centered Earth-fixed coordinates, referring to the WGS84 ellipsoid. As these coordinates have no direct relation to the observed structure, the resulting coordinates have been rotated, in a manner that the \(x\)- and \(y\)-coordinates are representing the longitudinal and transversal axes of the Neckartal bridge, respectively, and the \(z\)-component represents the vertical axis. Figures 16-18 show the resulting time series of the transformed point positions \(x,y\) and \(z\) for E2, E3 and E4. As can be seen in Figures 16-18, besides several short wave vibrations, there are also superposed significant low-frequency oscillations resulting from unknown sources, but that could be caused by a varying dilution of precision as indicated by [PERSON] and [PERSON] in [46]. Furthermore, the wind forces the bridge to swing, and temperature effects cause strains in the load-carrying concrete pillars. Oscillations induced by the heavy traffic on the Autobahn A81 and multipath effects could be further sources of these long wave signals. For example, [PERSON] et al.