## 4 Discussion
### Localization Accuracy and Precision  
In the first set of experiments, which were carried out with a fully distributed sensor configuration, the determined position of the disturbance and the localization precision can be directly read from a spatial-temporal representation of raw or adequately filtered data. Localization accuracy is basically determined by the accuracy of the mapping of bins to actual positions along the pipe. This can be done in a calibration procedure after installation of the fiber where the fiber is tapped in crucial places and the observed signals are assigned to the position. This procedure may be carried out with the shortest pulse length available yielding an expected accuracy determined by the spatial resolution of the system. Here, this amounts to 1 m / 7.9 = 0.13 m along the pipe for 10 ns pulses and the chosen helical configuration of the fiber. For excitation on the side of the pipe, which allows for an estimation of deviations in both directions along the pipe, the experimentally determined localization precision is visualized relative to the actual position of impact in Figure 12 for the three different pulse lengths. It amounts to \(\pm\) 51 cm for 100 ns, \(\pm\) 32 cm for 50 ns, and \(\pm\) 19 cm for 30 ns pulses. When employing a quasi-distributed sensor configuration knowledge of the propagation velocity in the material is a prerequisite to map the observed events to a position on the pipe based on the time  
Figure 11: Dispersion curves of group speeds for different acoustic modes propagating in cylindrical waveguides determined by numerical simulation for the given pipe geometry and material properties. Figure 12: Comparison of localization accuracy and precision for a fully distributed and a quasi-distributed sensor configuration consisting of two localized sensor regions along a pipe. Points of disturbances (**A**,**B**) are indicated as dashed lines for different pulse lengths. Localization precision values of the fully distributed configuration (blue bars) are directly given by the spatial resolution corresponding to the pulse length. For the quasi-distributed setup fiber-optically localized positions of impact are indicated (red diamonds) with corresponding error bars representing the localization uncertainty. (For localization around A using 50 ns pulses, slight shifts were introduced to the value of the pulse length to improve clarity of the representation). difference of signal onset. In practice, this value could be either taken from a theoretical consideration or from a calibration procedure with localized signals in known positions. For the sake of analyzing localization accuracy here, the relative deviation of the experimentally determined speed values from the theoretical value confirmed by numerical simulation is used as a measure for the deviation from the actual point of impact. The localization accuracy is depicted in Figure 12 for both positions of impact (front face and side of the pipe). The corresponding localization precision was derived from the measurement uncertainty by error propagation. It amounts to \(\pm 20\) cm to \(\pm 22\) cm independent of the evaluation procedure or pulse length. A summary of the deduced localization uncertainty for different sensor configurations and evaluation procedures is given in Table 2.  
However, the positions of impact determined for the quasi distributed configuration by evaluation of signal onsets hints at an additional systematic deviation to one side of the points of impact corresponding to systematically underestimated time differences between the two localized sensors. This is also evident in the trend to somewhat higher speed values (Table 1) deduced by this method. Further refinement of the evaluation procedure, e.g., consideration of other signal features may mitigate this effect as can be seen in the much higher position accuracy achieved when employing correlation procedures for data evaluation.