### Objective and Contributions  
Our study is motivated by the analysis of displacement measurements with GBR in the context of damage detection for bridges. We focus on output-only analysis to maintain regular bridge operation, which is a crucial advantage of remote sensors such as GBR compared to conventional sensors. Detecting deteriorations or damage to a bridge requires accurately estimating features from measurements. The success of a damage detection approach mainly depends on the uncertainty of these features. For example, it has been shown that the temperature variation of a bridge has a substantial effect on natural frequencies (e.g., [6]). Natural frequencies could not be used as features for damage detection without considering this effect. Additionally, the uncertainty of a feature also depends on the accuracy of the underlying measurements and the applied method for feature estimation. For example, natural frequencies estimated by frequency-domain methods can have insufficient resolution or may be biased by large time windows. Therefore, we propose an approach for feature estimation, which has the following objectives:  
* estimation of natural frequencies from GBR measurements while accounting for the individual accuracy per measurement point;
* analysis of the influences of temperature and vehicle weight on natural frequencies;
* assessment of requirements for feature uncertainty in the context of damage detection.  
In this study, we first provide a short overview of the measurement principle of GBRs to motivate the adapted approach for frequency estimation (see Section 2.1). We refer to previous studies for a more detailed description of GBRs (e.g., [1,2,18]). The measured displacements and their uncertainties are used as input data for our approach, as shown in Figure 1. After each vehicle crossing, a preprocessing step (Section 2.2.1) extracts the damped vibration. The parameters of these vibrations are then estimated in a least squares approach with a damped sinusoid model, which is described in Section 2.2.2. Since the vibrations may be disturbed by additional vehicle crossings or other influences, a test for goodness of fit filters the least squares results. The determination of test values for this test is explained in Section 2.2.3. Natural frequencies estimated with the least squares approach can be used for damage detection by testing for changes in the mean value (see Section 2.3). Section 3 shows the application of the least squares approach in a measurement campaign with a GBR and strain sensors. The results are also validated with the commonly applied Frequency Domain Decomposition (FDD). Similar to previous studies [5,6], the relationship between temperature and frequency is estimated with linear regression. Additionally, the proposed least squares approach enables a distinction between vehicle types by separately evaluating each vehicle crossing. Section 4 discusses these results in the context of damage detection with a hypothesis test. Finally, a conclusion is given in Section 5.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Features** & **Additional Sensors or Models** & **References** \\ \hline \multirow{2}{*}{Displacements} & FEM & [33] \\  & Total station & [34] \\ \hline \multirow{4}{*}{Natural frequencies} & GBR only & [26,27,35] \\  & FEM & [24,36,37] \\  & Accelerometer & [22,28,30,31,38,39] \\  & TLS and accelerometer & [40] \\  & FEM and accelerometer & [29] \\ \hline \multirow{2}{*}{Natural frequencies} & GBR only & [20,23,25,41] \\  & Accelerometer & [32] \\ \cline{1-1}  & FEM and accelerometer & [21] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Related work for comparison and evaluation of ground-based radar (GBR) in the context of modal analysis. Additional sensors or models for comparison are total stations, terrestrial laser scanners (TLS), accelerometers, or the Finite Element Method (FEM).