## 2 Methodology  
### Feature Extraction  
Reasonable feature value is critical to the capability of machine-learning algorithms, and this paper refers to the feature parameters of multipath/NLOS signal detection in supervised learning classifiers. Most of the current machine learning methods for multipath/NLOS detection adopt feature values at the observation data level. We only extract the feature parameters from the RINEX format file output by the GNSS receiver, including pseudorange, carrier phase, carrier-to-noise ratio (signal strength), and Doppler frequency shift, etc., which are all closely related to GNSS signal types. However, it is impossible for any single feature to effectively classify GNSS signals. Hence, a combination of different features is needed to ameliorate the classification accuracy [22; 38; 39; 40]. (1) Satellite elevation angle: It is a common method to assign weights to each observation value based on the satellite elevation angle to reduce the influence of multipath and NLOS signal reception on the positioning results. Generally speaking, satellite signals from high elevation angles are less likely to be blocked and reflected by buildings, but this is not always the case in reality. Due to the height and distribution of buildings in urban areas, satellite signals at high elevation angles may also be NLOS signals, while signals at low elevation angles may be direct signals. Nonetheless, satellite elevation angle is still an important feature indicator to distinguish NLOS signals. (2) Carrier-to-noise ratio: The GNSS receiver will output the observations of the tracked satellite signal strength. According to the signal propagation theory, supernumerary propagation and reflection will increase the path loss of the GNSS signal. As an important indicator reflecting the signal quality, the C/N0 observation value is also a common parameter to alleviate the multipath effect. Similar to the elevation angle, the satellite signal strength or carrier-to-noise ratio also has a certain correspondence with the type of signal. The signal strength of the satellite received by the survey antenna is usually higher in an open environment. However, the magnitude of C/N0 does not have a clear correspondence with the type of GNSS signal in a multipath environment, because constructive multipath will increase the received signal, while destructive multipath reduces signal strength. (3) Pseudorange residual: When there are more observation equations than unknown parameters and the position estimation is accurate enough, the magnitude of the pseudororange residual can reflect the inconsistency between the pseudorange measurements and the geometric distance of the satellite. In addition, multi-constellation GNSS integrated positioning increases the number of available observation satellites and observation redundancy. Therefore, the pseudorange residual can be used as an indicator to detect the quality of GNSS signals. (4) Pseudorange rate consistency: The pseudorange observations originate from the receiver code tracking loop, and the Doppler shift of the signal is determined by the receiver frequency tracking loop. Compared with the code tracking loop, the multipath/NLOS signal has less influence on the frequency tracking loop, so the consistency between the pseudorange change rate and the Doppler frequency shift can reflect the interference degree of the reflected signal. Its formula is expressed as:  
\[\zeta=|\Delta\rho-\dot{\rho}\cdot\Delta t| \tag{1}\]  
where \(\Delta\rho\) and \(\Delta t\) represent the pseudorange variation and time interval between adjacent epochs, respectively. According to the Doppler effect, the pseudorange rate \(\dot{\rho}\) is calculated from the Doppler shift. \[\dot{\rho}=-\lambda_{i}f_{D_{i}} \tag{2}\]  
where \(\lambda_{i}\) and \(f_{D_{i}}\) indicate the wavelength of frequency \(i\) and the Doppler shift in Hz, individually.