## 2 Literature Study
### Analysis of the Evaluated Track Quality Indices  
Many of the above introduced track quality indices share characteristics: (i) the basic concept, (ii) whether or not all track geometry parameters (Table 1) are considered, and (iii) the necessity of adjustment factors such as calibration or weighting coefficients (not considering constant factors which solely scale the results). Three major groups can be distinguished in the basic concept of the TQIs context: indices based on standard deviations (in Table 5: \"sd\"), indices converting the number of threshold exceedances (\"threshold\"), and indices which use other approaches (\"miscellaneous\"). According to this classification, the analyzed indices are listed in Table 5.  
Three of the analyzed track quality indices--Isolated defects, K-value, w5--convert the number of threshold exceedances into a TQI. Since indices of this kind merely count the number of defects while disregarding the severity of them, the informative value of these quality figures is limited, regardless of whether raw signals (Isolated defects, w5) or standard deviations (K-value) are evaluated. With eight examples, the majority of analyzed track quality indices are based on standard deviations: CoSD, Chinese TQI, CN's TQI, J coefficient, Q-value, Netherlands Q, TGI, and OTGI share this approach. As the standard deviation of a signal depends on the number of defects within the considered segment as well as the amplitudes of the errors, these indices are better suited to rate the overall track quality than indices counting threshold exceedances. A downside of the standard deviation is that it may deliver disproportionately high values for gauge and twist in curves (Section 4, Figure 8). Tight bends frequently exhibit an increased nominal track gauge for improved track guidance [36], while transition elements between straight sections and curves typically feature a rising outer rail to mitigate lateral accelerations, which by default creates a twist [37]. Consequently, the standard deviation of gauge and twist inevitably yields higher (worse) values in these areas, even if track quality is perfect. However, gauge widening and transition elements are technical necessities and a TQI that is intended to rate the overall track condition should not equalize them with track defects. The remaining indices--MDZ-a, R\({}^{2}\), FRA TQI--neither rely on threshold exceedances nor on standard deviations. Instead, they make use of different concepts. Regarding the utilization of different track geometry parameters, two of the analyzed indices aggregate all signals (Chinese TQI, w5) while others only include a selection of them or do not define it. From a mathematical perspective, merging signals of various parameters (or derivates such as standard deviations) is problematic, since they typically scatter in different amplitude ranges. Thus, signals which permissibly exhibit comparably high absolute values (e.g., longitudinal level) are overrepresented in the final TQI. Some track quality indices depend on calibration or weighting factors, which are either fix values (e.g., J coefficient), depend on the line speed (e.g., K-value), the track type (e.g., OTGI), or can be set by the infrastructure manager (e.g., CoSD). While for many TQIs reference values for their calibration factors are provided, the exact meaning and determination of these coefficients is often unknown. This hampers the application of the index in other networks. To evaluate how the analyzed track quality indices perform on real data, each of them is calculated for the 5-km test section and plotted (Figure 3). This ballast track section comprises a sequence of curves and straight segments, which are indicated in the plot by the super elevation. If an index does not specify the required geometry parameters, all signals are included. If an index only defines individual TQIs (e.g., the track roughness index R\({}^{2}\)), the holistic TQI is assumed to be the average of the