## 2 Materials and Methods
### Data Preparation and Processing
#### 2.4.3 Curve Fitting Methodology  
To accurately analyze and integrate the data obtained from LIDAR sensors into the model, the measured intensity values must be correlated with the optical power reaching the detector. This relationship is derived from Equation (1), which represents the fundamental optical power equation of LIDAR. In LIDAR systems, the optical power reaching the detector exhibits a nonlinear dependence on distance, atmospheric absorption, reflectivity, and other environmental factors. Therefore, for precise analysis and modeling, intensity data must be transformed into physically meaningful quantities (e.g., optical power). The intensity values obtained from LIDAR sensors are influenced by the characteristics of the sensor's electronic and physical components. To establish a relationship between the digital data and the optical power reaching the detector, a transformation that accounts for the effects of these components (e.g., ADC, transimpedance amplifier, photodetector) is necessary. This transformation ensures that intensity values are converted into a physically consistent representation (e.g., optical power in Watts). The process of computing optical power from intensity values is described by Equation (3):  
\[\mathrm{P_{optical}}=\mathrm{I_{digital}}\frac{\mathrm{V_{ref}}}{2^{n}-1} \frac{1}{\mathrm{R_{f}}}\frac{1}{\mathrm{R}} \tag{3}\]  
Here, \(\mathrm{I_{digital}}\) represents the digital output of the ADC (ranging 0-255), \(\mathrm{V_{ref}}\) denotes the reference voltage of the ADC (3.3 V), n indicates the resolution of the ADC (8 bits), \(\mathrm{R_{f}}\) refers to the load resistance (1 k\(\Omega\)) of the transimpedance amplifier responsible for current-to-voltage conversion. R (0.8 A/W) represents the sensitivity of the photodetector. In the first step, the intensity values were converted into voltage using the reference voltage and resolution of the ADC. The resulting voltage was then converted into a current through the load resistance of the transimpedance amplifier and ultimately transformed into optical power, reaching the detector based on the sensitivity of the photodetector. Furthermore, LIDAR sensors typically collect data from multiple channels using detector arrays. In this study, the intensity measurements provided by the sensor represent a single data point, which corresponds to the average value across all channels. Therefore, the intensity values obtained from the LIDAR sensor were analyzed under the assumption that they reflect the mean intensity of all detector channels. This approach not only simplifies data processing but also aligns with the physical characteristics of the intensity data output by the LIDAR device used in the experimental setup. Curve fitting serves as a critical tool for aligning these intensity values with the fundamental LIDAR equations. These transformation and curve fitting processes play a key role in ensuring that LIDAR data are analyzed in accordance with physical principles and effectively utilized in modeling applications. In this study, distance, angle, and reflectivity coefficient values were provided as input parameters to the GPR model. The same parameters were also applied as inputs to Equation (1), the fundamental optical power equation of LIDAR systems. This approach facilitated the derivation of a conversion function that links both theoretical and experimental data. The GPR model predicts intensity values based on the input parameters, and these predictions are converted into optical power values at the detector using Equation (3). Simultaneously, theoretical optical power values are computed using Equation (1). A curve fitting process was then applied between these two sets of optical power values to formulate a transformation equation that aligns the experimental intensity data with the theoretical optical power.