# A Post-Processing Multipath/NLoS Bias Estimation Method Based on DBSCAN
###### Abstract  
Positioning based on Global Navigation Satellite Systems (GNSSs) in urban environments always suffers from multipath and Non-Line-of-Sight (NLoS) effects. In such conditions, the GNSS pseudorange measurements can be affected by biases disrupting the GNSS-based applications. Many efforts have been devoted to detecting and mitigating the effects of multipath/NLoS, but the identification and classification of such events are still challenging. This research proposes a method for the post-processing estimation of pseudorange biases resulting from multipath/NLoS effects. Providing estimated pseudorange biases due to multipath/NLoS effects serves two main purposes. Firstly, machine learning-based techniques can leverage accurately estimated pseudorange biases as training data to detect and mitigate multipath/NLoS effects. Secondly, these accurately estimated pseudorange biases can serve as a benchmark for evaluating the effectiveness of the methods proposed to detect multipath/NLoS effects. The estimation is achieved by extracting the multipath/NLoS biases from pseudoranges using a clustering algorithm named Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The performance is demonstrated using two real-world data collections in multipath/NLoS scenarios for both static and dynamic conditions. Since there is no ground truth for the pseudorange biases due to the multipath/NLoS scenarios, the proposed method is validated based on the positioning performance. Positioning solutions are computed by subtracting the estimated biases from the raw pseudoranges and comparing them to the ground truth. multipath; non-line-of-sight; pseudorange bias; clustering algorithm 20242611. 10.3390/s24082611 10.3390/24082611 10.  
into three groups based on the specific stage of the user receiver at which detection and/or mitigation are applied:  
The first group of solutions includes antenna-based techniques. In scenarios involving multipath/NLoS effects, the reflected GNSS signals may undergo changes in polarization and reception angles compared to the direct signals. To mitigate this issue, researchers developed advanced antenna designs, including choke rings, dual-polarized antennas, and array antennas, to minimize the reception of reflected signals [2; 4; 5]. The second family of multipath/NLoS detection and mitigation techniques relies on signal processing. Multipath occurs when the signals reflected from surfaces reach the receiver along with the direct signals. In GNSS baseband signal processing, the shift in auto-correlation functions caused by reflected signals can overlap with the auto-correlation function of the direct signal. As a result, the computed auto-correlation function in the Delay-Lock Loop (DLL) will be distorted due to this overlapping. To address this, various advanced signal tracking techniques have been proposed for identifying and mitigating multipath interference [6; 7; 8; 9]. The third group of techniques operates within the positioning unit to detect and mitigate multipath/NLoS interference. Pseudorange biases induced by multipath/NLoS effects pose a threat to the consistency between the pseudorange measurements and the corresponding navigation solutions. Some approaches utilize the chi-squared test for detecting and mitigating the impact of multipath/NLoS effects [10]. Additionally, 3D city models and cameras are employed to establish the propagation model of reflected signals [11; 12]. Furthermore, researchers explore the potential of machine learning algorithms to establish relationships between multipath/NLoS effects and other indicators, such as satellite elevations/azimuths and the carrier-to-noise-density ratio (\(C/N_{0}\)) [13; 14; 15]. In an effort to contribute to the development of methodologies mitigating multipath/NLoS effects, this research proposes a post-processing solution for estimating the pseudorange biases caused by these phenomena.