Multipath Detection in GNSS Using Differential Corrections and Machine Learning-Based Classification

As mentioned in the previous section, to collect satellite data, the system employs a combination of a mobile receiver (Rover) and a fixed reference station (Base station). The Rover is specifically designed for field deployment, equipped with a high-precision u-blox ZED-F9P GNSS receiver and a specialized polarized antenna that effectively minimizes the impact of multipath interference. Figure 2 shows the pictures of polarized antenna and u-blox ZED-F9P GNSS receiver used in our experiments. This setup ensures reliable and accurate data collection in dynamic environments.

Figure 2.

Polarized antenna and u-blox receiver module

As Differential GNSS (DGNSS) requires both a mobile and a stationary reference receiver, the Base station plays a critical role. It must be placed at a location with a precisely known position and minimal multipath interference. For this purpose, we use a Base station that is part of Vietnam’s official GNSS network, managed by the Ministry of Natural Resources and Environment. This choice ensures stable and accurate correction data for high-precision GNSS applications.

In our experiments, data are collected along the path between two buildings, as shown in Figure 3. Specifically, the u-blox positioning module was connected to the polarized antenna and a computer to collect satellite data in this area. During the data collection process using the u-center software, positioning accuracy metrics such as 3D accuracy, 2D accuracy, PDOP, and HDOP showed very high values. This indicates that the area between two buildings in our experiment is heavily affected by multipath interference.

Figure 3.

Data collection at an area between two buildings in our experiment

Once the rover receiver is in the field, satellite data collection begins using RTKNAVI, a component of the RTKLIB software suite (Version 2.2.1 is used in our experiment). RTKNAVI provides real-time monitoring and logging of GNSS data. The data acquisition process involves two primary data streams. The first is raw satellite signal data collected by the Rover receiver, which is transmitted to a computer through a serial interface. Within RTKNAVI, the appropriate communication parameters must be configured to ensure seamless data logging. These raw data are saved in the UBX format, a proprietary u-blox binary format designed for efficient storage of GNSS measurements. The second data source is the correction information from the Base station. RTKNAVI is set up to receive these corrections using the NTRIP (Networked Transport of RTCM via Internet Protocol). Through a network connection, the Rover accesses real-time RTK correction data broadcasted by the Base station. These correction data are saved in the standard RTCM3 format, which is widely used in GNSS for differential corrections.

These two data streams, Rover UBX files and Base station RTCM3 files, form the raw input for subsequent processing. In the following stage, the system decodes and standardizes these files to ensure consistent formatting and compatibility. This standardization step is essential as it prepares the data sets for the processing procedures used in subsequent phases, enabling accurate positioning and advanced GNSS analysis.

The collected satellite data are stored in two specialized file formats: UBX and RTCM3, each requiring a different processing method. For UBX files, which use a proprietary binary protocol developed by u-blox for their GNSS/GPS receiver modules, the program leverages the Python pyubx2 library to decode and extract relevant data.

As highlighted earlier, precise GNSS positioning depends on two key range measurements per satellite: pseudo-range and carrier phase. The program extracts these critical fields from the UBX file to support downstream positioning computations. In addition, it retrieves additional information, such as timestamp, satellite constellation, satellite ID, and signal type, all of which are valuable for in-depth analysis and quality assessment.

The main steps in processing UBX data are as follows:

• Convert raw binary data into a readable string format for easier observation and extraction.

• Extract key fields, including: Time (signal reception time), Satellite Group, Satellite Group Number (ID within the group), Pseudo-range (P1/C1), Carrier phase (L1)

• Filter and retain only the primary satellite constellations of interest: GPS

For processing RTCM3 data (Radio Technical Commission for Maritime Services, Version 3 standard), the Python pyrtcm library is available. However, unlike UBX files, RTCM3 data does not directly provide essential GNSS measurements such as pseudo-range, carrier phase, or signal type. Extracting this information from RTCM3 messages is complex and time consuming and may not yield high accuracy. To overcome these limitations, RTCM3 data are first converted into OBS files (RINEX observation format) using RTKCONV, a tool from the RTKLIB software suite. RINEX (Receiver Independent Exchange Format) is a widely accepted and standardized format that simplifies GNSS data handling and ensures compatibility with various post-processing tools. This conversion ensures that the RTCM3 correction data are transformed into a standardized and accessible format, allowing efficient integration with the Rover observation data in later processing stages.

To simplify the program and improve the organization of the data, each RTCM3 file is split into four separate OBS files corresponding to the four main satellite systems: GPS, GLONASS, Galileo, and BeiDou, just as with the UBX data. The OBS file (RINEX observation format) contains the key fields required for GNSS data analysis, making it well suited for processing. It includes information such as the signal reception time (e.g., 24 4 26 9 51 13.000000, representing year, month, day, hour, minute, and second), the satellite constellation, and IDs (e.g., 8C 1C 2C 4C 5C 7C 8C 10C 13C, indicating 8 satellites with IDs C1, C2, C4), and essential measurements like pseudorange (C2) and carrier phase (L2). The program extracts these critical data fields and formats them to ensure compatibility between the Base station and Rover data sets. One key aspect of this process is time synchronization. The UBX file stores timestamps as the number of seconds since the most recent Sunday, whereas the OBS file uses absolute date and time. To align the two data sets, the program converts the OBS timestamps to the same time format used in the UBX files. This synchronization is vital for accurate differential processing in later stages, ensuring that measurements from both receivers correspond to the same epoch.

The final output of this satellite data processing step is the creation of two Excel data files: Base.xlsx and Rover.xlsx, each containing the same standardized data fields:

• “Time” (synchronized time)

• “Satellite-Number” (satellite ID)

• “P1/C1” (pseudo-range)

• “L1” (carrier phase)

After preprocessing the satellite data, the Rover and Base station datasets are merged based on two key fields: “Time” and “Satellite-Number”. Ensuring consistency in these fields across both datasets is essential for accurate alignment and meaningful analysis. The merged data set combines the corresponding measurements from Rover and Base for each satellite at each epoch, resulting in a unified data structure that includes the following fields.

• “Time”

• “Satellite-Number”

• “P1/C1-r”: pseudo-range from Rover

• “L1-r”: carrier phase from Rover

• “P1/C1-b”: pseudo-range from Base

• “L1-b”: carrier phase from Base

Once Rover and Base data sets have been successfully merged, the program applies the Differential GNSS (DGNSS) technique to improve positioning accuracy by removing common-mode errors. In DGNSS, it is assumed that the distances from a satellite to the Base station and to the Rover are significantly greater than the distance between the two receivers. This assumption allows us to consider the signal paths from the satellite to both receivers as nearly identical, meaning that many errors, such as ionospheric and tropospheric delays, are shared and can effectively be canceled.

To do this, the program first calculates the single difference of the pseudo-range measurements for each satellite i: (1) Ri=ρib−ρir {R_i} = \rho _i^{\left( b \right)} - \rho _i^{\left( r \right)} where ρib \rho _i^{\left( b \right)} and ρir \rho _i^{\left( r \right)} are the pseudo-range measurements from satellite i to Base and Rover, respectively. This single difference R_i eliminates the most common transmission-related errors. However, residual errors such as multipath interference or receiver-specific biases may still exist.

To further reduce these residual errors, the program computes the double difference by selecting another satellite k and calculating: (2) R=Ri−Rk=ρib−ρir−ρkb−ρkr R = {R_i} - {R_k} = \left( {\rho _i^{\left( b \right)} - \rho _i^{\left( r \right)}} \right) - \left( {\rho _k^{\left( b \right)} - \rho _k^{\left( r \right)}} \right)

This double differencing removes remaining biases and isolates errors unique to specific satellite-receiver paths, especially those caused by multipath. Repeating this process across multiple satellite pairs, the program generates a time series of double-differenced values, which serve as input for subsequent processing steps.

This DGNSS method is applied to both pseudo-range and carrier phase data. For pseudo-range, the difference between Rover and Base for satellite i is computed as follows (3) R=P1/C1r−P1/C1b R = P1/C{1^{\left( r \right)}} - P1/C{1^{\left( b \right)}}

Then, for each satellite, this value is subtracted from the differential measurements of all other satellites to compute the pseudo-range double difference, forming the foundation for advanced analysis such as noise detection and quality assessment.

The same differential approach used for pseudo-range measurements is also applied to the carrier phase. Specifically, the carrier phase difference between the Rover and the Base station for satellite i is calculated as follows (4) R=L1r−L1b R = L{1^{\left( r \right)}} - L{1^{\left( b \right)}} where L1^(r) and L1^(b) represent the L1 carrier phase measurements from the Rover and Base station, respectively. For a selected reference satellite, the program then calculates the double difference by subtracting R_i from the carrier phase differences of all other satellites. This process yields a set of values that reflect the relative error deviations between satellite pairs.

These computed deviations are subsequently organized into a time series that captures how errors between satellite pairs vary over time. Representing the data in this time series format provides several important advantages. First, it allows intuitive visualization and analysis of trend and error fluctuations, enabling the detection of patterns or anomalies that may not be evident in static data. More importantly, this time-series representation serves as a critical input for advanced algorithms aimed at detecting multipath interference. Multipath errors often exhibit characteristic temporal behaviors, and by modeling the evolution of error values over time, the algorithm can more effectively identify and isolate corrupted signals.

In summary, transforming differential measurements into a time series structure not only enhances interpretability and analytical depth but also plays a vital role in supporting accurate and robust multipath detection in subsequent processing stages.

For each satellite i, we construct a comprehensive feature vector that combines both features in the DGNSS-based and observation domain. First, we form satellite pairs by calculating the double differences in the pseudo-range and carrier phase measurements between the satellite i and every other satellite in view. From these pairwise differences, we compute statistical features such as the minimum, maximum, mean, and median for both pseudo-range and carrier phase values. These statistics capture the variation in the GNSS signal paths relative to other satellites, reflecting potential anomalies or irregularities in the satellite i’ signal.

In addition to the pairwise characteristics, we extract statistical summaries per satellite for satellite i based on its own observation data. These include the minimum, maximum, mean, and median values of parameters such as azimuth angle, elevation angle, Doppler shift, and carrier-to-noise ratio (C/N₀).

The resulting feature vector for the satellite i thus encapsulates both the measurement discrepancies between the satellites and the geometric and signal quality characteristics specific to that satellite. This rich representation is well-suited for downstream tasks such as multipath detection, anomaly classification, or signal quality assessment.

After labeling each epoch’s DGNSS-derived vector as either Clean or Noise, we evaluate various classification models using this labeled data set. The evaluation process involves the following main steps:

• Feature Preparation: For each epoch, the input is a vector containing corrected pseudorange and carrier-phase measurements from all visible satellites, or a fixed-size representation derived from these. All vectors are normalized or standardized and paired with their corresponding Clean/Noise labels.

• Model Selection and Hyperparameter Tuning: We explore multiple model families, tuning key hyperparameters using cross-validation (e.g., 5-fold stratified). The classification models are explored including Random Forest, Decision Tree, Gradient Boosting, Bagging, AdaBoost, and Support Vector Machine. For each model, we use GridSearchCV (or randomized search) with cross-validation folds (e.g., 5-fold stratified) in the training set to select optimal hyperparameters. Early stopping (to boost) or class-weight adjustment may be applied if the classes are imbalanced.

• Training and validation:

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    Data Split: Divide the data set into training, validation, and test sets (e.g, 70% train, 30% test), maintaining the distribution of the labels through stratification.

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    Model Training: For each model and hyperparameter configuration, train using the training folds and evaluate on the validation folds. Select the best configuration based on the F1-score in the validation data.

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    Final Model: Retrain the chosen model on the combined training+validation sets with those optimal hyperparameters, and then evaluate on the held-out test set.

• Evaluation metrics: We report the following metrics for both the Clean and Noise classes: accuracy, precision, recall, and the F1-score.

• Analysis and Insights:

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    Model comparison: Evaluate which models best capture nonlinear relationships among DGNSS-derived features.

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    Feature Importance: For tree-based models (Random Forest, Gradient Boosting), analyze feature importance to identify key pseudorange or carrier-phase patterns that correlate with multipath or noise. The feature importance analysis was conducted and showed that features related to carrier-phase double-difference statistics as standard deviation and median values within satellite pairs had the highest importance, followed by pseudo-range double-difference metrics, while individual raw measurements contributed less to the final decision boundaries.

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    Overfitting check: If overfitting is detected (e.g., high training but low validation accuracy), consider adding regularization or applying dimensionality reduction techniques such as PCA before retraining.

Instead of directly classifying a single-epoch vector, this approach transforms temporal patterns of DGNSS-derived vectors into images or graphs, and then applies image-based feature extraction and classification.

• Time-series to Image Transformation: For each target satellite i, a sliding window of duration T seconds (e.g., T = 120 s) is applied to capture its error deviations relative to a set of reference satellites. Within each window, an error deviation series is computed by taking the difference (or residual) between the pseudorange or carrier-phase measurements of the target satellite and those of the references or by comparing against a DGNSS-based prediction. These deviations are then visualized as 2D plots—such as error vs. time—or as more advanced representations like recurrence plots, correlation matrix heatmaps, or connectivity graphs, which help emphasize patterns indicative of anomalous multipath effects.

• Image preprocessing: All images are standardized to a uniform grayscale size (e.g., 128×128 or 224×224 pixels). Axes and scales are normalized to ensure consistency across samples, with cropping or padding applied as needed to maintain fixed dimensions. Optionally, data augmentation techniques such as random shifts or noise injection can be used to improve model generalization.

• HOG + SVM classification: In this approach, Histogram of Oriented Gradients (HOG) is applied to each image to extract fixed-length feature vectors that capture local gradient patterns and edge orientations. These HOG descriptors serve as input to a Support Vector Machine (SVM) classifier. The SVM model’s hyperparameters—including the kernel type (e.g., RBF or linear), regularization parameter C, and kernel coefficient γ—are optimized using GridSearchCV. Model evaluation is conducted on a stratified train/validation/test split, using metrics such as precision, recall, F1-score, and ROC AUC to assess classification performance.

• CNN-based classification: We employ a convolutional neural network (CNN) architecture designed to process grayscale images of size 128×128×1. The model consists of several convolutional blocks using 3×3 filters, each followed by ReLU activation and MaxPooling layers, and concludes with one or more dense layers (e.g., 128 units) and a final output layer using either a sigmoid function for binary classification or softmax for multi-class scenarios. The network is trained using the Adam optimizer with a learning rate of 1e-3 or 1e-4, and binary cross-entropy is used as the loss function. Training is performed in mini-batches (batch size 32 or 64), with early stopping based on validation loss or other performance metrics to prevent overfitting. Data augmentation techniques may be applied during training to improve generalization. After tuning hyperparameters such as the number of filters, network depth, and dropout rate, the final model is evaluated on a held-out test set using standard metrics like accuracy, precision, recall, and F1-score.

In this approach, we integrate both raw observation features (e.g., C/N0, Doppler, elevation, azimuth) and DGNSS-derived metrics (e.g., corrected pseudorange and carrier-phase residuals) to construct a comprehensive feature vector for each satellite at each epoch. This combined representation captures both the instantaneous signal quality and the behavior of error corrections.

• Feature Construction and Preprocessing: This step involves collecting both observation and DGNSS-derived features for each satellite at each epoch. Observation features include C/N0, Doppler shift, elevation angle, azimuth, signal-to-noise ratio (SNR), and multipath indicators if available from the receiver. DGNSS features consist of corrected pseudorange and carrier-phase residuals, along with optional statistical summaries such as the standard deviation of residuals over recent epochs. All features are then normalized using either standard scaling (zero mean, unit variance) or robust scaling based on the training set. Feature engineering techniques are applied to enhance the input representation, including the computation of interaction terms (e.g., residual divided by C/N0), and the generation of time-series statistics such as mean, variance, or trend over a sliding window of previous epochs. Categorical variables, such as signal bands, are encoded using one-hot encoding. If the resulting feature space is high-dimensional, optional dimensionality reduction methods like principal component analysis (PCA) or recursive feature elimination can be used to improve generalization and reduce overfitting.

• Model Selection and Hyperparameter Tuning: A variety of model families are explored to classify the combined feature vectors. Tree-based ensemble methods such as Random Forest and Gradient Boosting (e.g., XGBoost, LightGBM, HistGradientBoosting) are employed, with key hyperparameters including the number of trees, maximum depth, learning rate, and subsampling ratios carefully tuned. Support Vector Machines (SVM) are also considered for data sets with moderate feature dimensions, where tuning involves selecting the appropriate kernel type, regularization parameter C, and kernel coefficient γ. Logistic Regression serves as a baseline, with both L1 and L2 regularization options. Additionally, small feedforward neural networks (MLPs) with 2–3 hidden layers are tested, where the number of units per layer, activation functions, dropout rates, and learning rates are subject to tuning. For further performance enhancement, model stacking is applied by combining multiple base learners (e.g., Random Forest, SVM, and MLP) using a meta-learner. Hyperparameter optimization is conducted via GridSearchCV or Bayesian optimization with cross-validation, with F1-score used as the primary metric, particularly in the presence of class imbalance.

• Training and evaluation: The data set is first stratified by label and split into training, validation, and test sets to preserve class distribution. Cross-validation is performed on the training set to identify the optimal hyperparameters for each model. Once the best configuration is determined, the model is retrained using the combined training and validation sets to maximize the available data for learning. Final performance is then evaluated on the held-out test set. The evaluation includes standard classification metrics such as accuracy, precision, recall, and F1-score, with particular emphasis on F1-score to account for potential class imbalance.

The evaluation metrics used in this study include precision, recall, and F1-score for each predicted class on the test data set. Among these, accuracy is considered the most important metric as it reflects the overall performance of the model in each experiment and serves as a key indicator of its practical applicability.

The experiments were carried out in two sessions: the first lasted 30 minutes and the second lasted 2 hours. During both sessions, 11 GPS satellites continuously transmitted signals without interruption. A total of 2312 samples were collected. Of these, 350 samples were labeled as “clean”, while the remaining samples were affected by multipath interference and labeled as “noise.”

This study presented an integrated framework for multipath detection in GNSS that combines DGNSS corrections with machine learning-based classification, enabling automatic identification and exclusion of satellites affected by signal reflections. By leveraging synchronized base–rover data, double-difference processing, and both raw and corrected observation features, the proposed methods achieved strong classification performance across three complementary approaches. The experimental results demonstrate that ensemble learning, particularly the Random Forest model, delivers the highest accuracy, reaching up to 99.75% when using combined feature vectors, while CNN outperforms traditional classifiers in image-based detection. These findings confirm that the proposed approach effectively captures multipath-induced distortions in both statistical and visual domains, offering a promising direction for improving signal integrity and positioning reliability in challenging urban environments.

However, the approach is most effective in controlled or survey-specific environments, where users have adequate time and specialized equipment to collect the required data. In contrast, for everyday positioning scenarios, where users are constantly in motion and typically lack access to advanced data collection tools, the accuracy of the proposed indicators may degrade significantly. To enable broader applicability including both professional and daily use cases, the methodology and data acquisition processes will need further refinement.

In our experiment implementation, we applied a conservative constant elevation angle derived from the shortest satellite–obstacle geometry. This choice intentionally overestimates the blocking elevation angle to ensure that all potentially obstructed satellites are categorized as “Noise.” While this simplifies the visibility model, the experimental results indicate that it does not critically affect the final classification performance. The combination of DGNSS-derived features and machine learning classification compensates for the coarse geometric model, as the models learn signal-based characteristics rather than relying solely on the visibility mask. In future work, we plan to incorporate azimuth-dependent elevation angles extracted from detailed obstacle geometries (e.g., pixel-level 3D building models or CAD-based profiles) to further refine the labeling process and improve general applicability in complex urban environments.

In this study, the primary focus was to develop and evaluate a robust multipath/NLOS detection framework using DGNSS-derived features and machine learning, while positioning performance was not assessed as part of the experimental scope. The results therefore reflect the classification capability of the proposed methods rather than their impact on final positioning outputs. In future work, we will integrate the detection module into a complete DGNSS positioning pipeline and perform a quantitative comparison using three configurations: raw GNSS data, DGNSS corrections, and DGNSS with detected NLOS satellites excluded. This evaluation will allow us to directly measure the contribution of the proposed detection strategy to positioning accuracy and demonstrate its practical benefits in real-world applications.

To enhance the applicability and robustness of this research in both specialized and everyday contexts, several future directions are proposed.

First, the application of advanced machine learning techniques offers significant potential. Deep learning models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs) including LSTMs, and Transformers can be explored to automatically extract meaningful features from raw GNSS signals or image-based representations, especially when larger data sets are available. In addition, unsupervised and semi-supervised learning methods could be employed to take advantage of unlabeled data collected in the field, reducing reliance on manual labeling. Domain adaptation and transfer learning techniques are also promising, as they enable models trained in one region or environment to adapt effectively to new conditions, improving scalability and cross-region generalization.

Second, integrating 3D environmental modeling and simulation can greatly enhance training data quality and detection accuracy. Techniques such as ray-tracing, combined with 3D models of buildings and terrain, can simulate realistic multipath effects and generate rich synthetic data sets. Incorporating 3D map data and geographic information systems (GIS) can also help identify areas with high multipath risk and feed that information into the detection pipeline to improve performance.

By pursuing these directions, the research can evolve into a more comprehensive and practical solution for GNSS multipath detection across a wide range of applications.