The quality of Galileo system services is affected by the accuracy of distance determination from the user’s application to the individual satellite. The goal of our research was to find out what influence the accuracy of distance determination between the user’s application of the Galileo system and the cooperating satellites of the Galileo system has on the ability to determine the location of the user’s application. A solution based on Groebner’s algebraic approaches was used to determine the receiver user’s position. When creating distance measurement error models between the Galileo system user’s receiver and cooperating satellites, we assumed that the values of those errors considered all factors that affected the accuracy of those distance measurements. To evaluate the algorithms, we used a statistical set of 500 simulation results to determine the positioning of the user’s application of the Galileo system. If the distances between the user’s application and the individual satellite were measured accurately, then the user’s application coordinate errors had values between 1.86 × 10⁻⁹ m and −1.8 × 10⁻⁸ m. These errors should be equal to zero. The positioning error was caused by a numerical error in the calculation due to the software used. If the errors of distance determination from the user’s application to the individual satellite varied from −0.05 m to 0.09 m, then the error in determining the positioning of the user’s application of the Galileo system was from 0.0 m to 1.2 m. If the distances of the user’s receiver to the satellites were measured with errors greater than 0.09 m, the errors in determining its position were much larger. The simulation results confirmed the known fact that the satellites’ geometry influences the accuracy of determining the location of the user’s application. In the following research, we will solve the problem of how to reduce the sensitivity of the mentioned algorithms when determining the position of the satellite navigation system receiver due to errors in determining the distance from the user’s application to the individual satellite.

This article addresses anomaly detection in multichannel spatiotemporal data under strict low-false-alarm constraints (e.g., 1% False Positive Rate, FPR), a requirement essential for safety-critical applications such as signal interference monitoring in sensor networks. We introduce a lightweight, interpretable pipeline that deliberately avoids deep learning dependencies, implemented solely in NumPy and scikit-learn. The core innovation lies in fusing three complementary anomaly signals in an ensemble: (i) Principal Component Analysis (PCA) Reconstruction Error (MSE) to capture global structure deviations, (ii) Local Outlier Factor (LOF) on residual maps to detect local rarity, and (iii) Monte Carlo Variance as a measure of epistemic uncertainty in model predictions. These signals are combined via learned logistic regression (F*) and specialized Neyman–Pearson optimized fusion (F** and F***) to rigorously enforce bounded false alarms. Evaluated on synthetic benchmarks that simulate realistic anomalies and extensive SNR shifts (±12 dB), the fusion approach demonstrates exceptional robustness. While the best single baseline (MC-variance) achieves a True Positive Rate (TPR) of ≈0.60 at 1% FPR on the 0 dB hold-out, the fusion significantly raises this to ≈0.74 (F**), avoiding the performance collapse of baselines under degraded SNR (maintaining ≈ 0.62 TPR at −12 dB). This deployable solution provides a transparent, edge-ready anomaly detection capability that is highly effective at operating points critical for reliable monitoring in dynamic environments.

This paper contains a model of the flying object (FO) flight trajectory in the geocentric coordinate system and a model of FO position measurement errors using a Global Navigation Satellite System (GNSS) receiver under interference conditions. The size of the FO coordinate errors in the horizontal and vertical planes ranged from +20.0 m to −20.0 m. This paper’s contribution is the creation of algorithms for processing GNSS signals under interference conditions based on the Savitzky-Golay filter and neural network. The simulation results confirmed that the Savitzky-Golay filter when applied in the GNSS receiver, can suppress FO position measurement errors. For example, if absolute FO position measurement errors due to GNSS interference were from 0.0 m to 5.0 m, and the mean square error of these errors was 0.441 m2, the Savitzky-Golay filter reduced them to a value from 0.0 m to 0.8 m, and the mean square error of these errors was equal was 0.0195 m2. In this case, the mean error value in the FO position after filtering with the Savitzky-Golay filter was 0.32 m, and the mean square error was 0.019 m2. Advanced machine learning techniques in the form of neural networks were also used to suppress errors from the output of the Savitzky-Golay filter. The simulation confirmed that if the FO position errors at the neural network’s input ranged from 0 m to +0.8 m, the neural network reduced them to 0.0 m to 0.5 m. The mean FO position error value was 0.12 m, and the mean square error was 0.0089 m2. The results of this study may contribute to more precise and reliable FO navigation and improve the use of GNSS systems in interference conditions.

This paper created a flight trajectory model of five uncrewed aerial vehicles (UAVs) in the geocentric coordinate system, provided the UAVs fly in the specified formation. Based on this model, equations for determining the position of a selected member of a group of UAVs were created, provided that the group communicates with each other in its telecommunications network. The simulation confirmed that if we know the exact coordinates of the four member UAVs of the group and their distances from the leader of the group, then the mean value of the error in determining its position in flight is equal to 0.044 m, and the variance is equal to 2.9 m². We consider these errors to be methodological errors of the proposed method. Next, we checked how the error of determining the position of the group leader depends on the distance measurement errors between the individual UAVs and the group leader. The simulation confirmed that if errors in measuring the distance between individual UAVs and the group leader are from 0.01 m to 12.0 m, the mean values of group commander position determination errors range from 0.11 m to 34.6 m. The simulation result showed that to accurately determine the group commander’s position, the distance measurement errors between individual UAVs and the group commander must be less than 1.9 m. The research results showed that the telemetry method can be used to determine the position of individual members of the UAV group. The advantage of this method is that it does not require the reception of signals from satellite navigation systems, which can be interfered with under certain conditions. The disadvantage of the method is the need to synchronize the time bases of individual UAVs that communicate in the telecommunications network.

This article contains an analysis to white noise interference. To conduct the research, models for both the E5 signal and white noise were developed and combined using an additive mixture. Using available data, spectral structures were established for the interference and then integrated into the E5 signal using the Matlab program. The objective of the study was to examine how white noise impacts the spectral power density of the E5 signal. The findings of this research can be utilized in the development of resilient receivers and signal architectures capable of withstanding this kind of disruption.

Global Navigation Satellite Systems (GNSS) constitute a critical positioning layer for intelligent transportation systems, including road mobility, aviation navigation, maritime operations, and emerging autonomous transport applications. The growing exposure of GNSS-enabled transport services to spoofing, jamming, and meaconing attacks creates a pressing need for deployable integrity-monitoring approaches capable of identifying interference without relying on specialized radio-frequency hardware or raw IQ signal access. This paper proposes a leakage-safe receiver-derived framework for GNSS interference recognition based exclusively on navigation-level and receiver-level observables available from standard commercial GNSS devices. The methodology integrates positioning trajectories, radial drift descriptors, local instability metrics, horizontal accuracy estimates, pseudorange-based statistics, Doppler-related variables, and integrity-oriented risk indicators extracted from NAV-PVT, RINEX, and MON-RF measurements. Using the publicly available JammerTest 2024 dataset, a comprehensive preprocessing and feature-engineering pipeline was implemented to construct window-level representations of interference-induced positioning degradation. To avoid overly optimistic performance estimates caused by temporal and scenario overlaps, model evaluation was performed using repeated scenario-group holdout splitting, ensuring strict separation between training and testing scenarios. Window-level classification was subsequently carried out using an ExtraTrees ensemble classifier on 2,939 integrity windows derived from 44,639 positioning samples across 24 spoofing, jamming, and meaconing scenarios. Under this leakage-safe evaluation protocol, the proposed framework achieved a mean classification accuracy of 62.86 % ± 9.58 % and a mean macro-F1 score of 0.5490 ± 0.0980 across repeated scenario-group splits. Feature-importance analysis identified radial drift descriptors, Doppler-related observables, and pseudorange-based statistics among the most discriminative receiver-derived variables. Although classification performance remained lower for meaconing than for spoofing and jamming, the results demonstrate that standard receiver outputs retain operationally meaningful information for interference-aware positioning monitoring even without direct signal-level access. The proposed framework provides a reproducible baseline for resilient GNSS integrity monitoring and practical interference recognition in intelligent transportation systems operating under degraded navigation conditions.