Diff-GNSS: Diffusion-Based GNSS Pseudorange Error Estimation for Accurate Positioning

Improving GNSS Performances in Location-Based Services through Synthetic Carrier-Phase Measurements

Abstract. Carrier phase observations enable millimeter-level GNSS positioning, but their continuity is frequently disrupted by signal blockages and cycle slips. This limitation is particularly critical for low-cost and smartphone receivers, where weak antennas, urban multipath, and duty cycling cause frequent phase gaps that prevent reliable ambiguity resolution. Before addressing the full complexity of mass-market observations, the prediction methodology must be validated under controlled conditions. In this work we investigate whether machine learning, supported by precise satellite orbits and clocks, can predict carrier phase observations during signal gaps with millimeter-level accuracy. Twenty-four hours of Galileo data from the TORI permanent station (SPIN3 network, Torino, Italy) are processed at 30 s sampling using GFZ final SP3 and CLK products. After forming the ionosphere-free combination, an iterative carrier-phase based estimator removes the receiver clock, tropospheric delay, and ambiguity, reducing the residuals to a median standard deviation of 60 mm. Synthetic gaps from 60 s to 1800 s are introduced (1045 gaps total) and four prediction strategies are compared: polynomial fitting (degrees 3 and 5), Fourier-augmented polynomial, Gradient Boosting Regression with satellite geometry features, and Gaussian Process Regression. The Gradient Boosting model achieves the best overall performance, reaching 4.4 mm RMS for 60 s gaps, 9.4 mm for 5 min gaps, and 21 mm for 30 min gaps, well below the half-wavelength threshold required for cycle slip repair. These results demonstrate that geometry-aware gap prediction is feasible at the sub-wavelength level, providing a validated foundation for extending the approach to low-cost and smartphone GNSS receivers.

Enhancing GNSS RTK positioning in complex scenarios: an extended robust strategy integrating random forest-based NLOS probability estimation

GNSS/eLoran Fusion-Based RAIM for Satellite-Deficient Environments

Global Navigation Satellite Systems (GNSS) provide essential positioning, navigation, and timing (PNT) services for a wide range of safety-critical applications. However, GNSS performance degrades significantly in satellite-deficient or interference-prone environments. To address this limitation, this study proposes a hybrid GNSS/eLoran integrity monitoring framework based on a simplified Receiver Autonomous Integrity Monitoring (RAIM) architecture. In the proposed method, GNSS observations from satellite constellations and range-equivalent measurements from the enhanced Loran (eLoran) terrestrial system are jointly processed using a weighted least-squares estimator. Integrity monitoring is performed through a global chi-square consistency test combined with a solution separation strategy for fault identification and exclusion. Horizontal Protection Level (HPL) is derived from the covariance of the estimation process to ensure bounded positioning error under nominal and fault conditions. Unlike conventional GNSS-only RAIM, the proposed framework enables improved redundancy and fault observability in satellite-deficient scenarios by incorporating heterogeneous terrestrial measurements. Simulation experiments consider satellite faults, eLoran measurement disturbances, and inter-system clock bias effects. Results demonstrate that the proposed method maintains reliable fault detection capability and ensures that positioning errors remain consistently bounded by the protection level under all tested scenarios.

A conformal prediction-based probabilistic weighting method for GNSS NLOS mitigation in urban canyons

In urban canyon environments, global navigation satellite system (GNSS) signals frequently suffer from building blockage and reflection, generating non-line-of-sight (NLOS) errors that significantly degrade positioning accuracy. Traditional elevation-angle and carrier-to-noise ratio (C/N0) weighting methods rely on indirect signal quality indicators, and fail to reliably identify NLOS satellites in dense urban settings; existing machine learning approaches apply classifier-derived LOS probabilities directly to satellite weighting, but these probabilities often lack accuracy in complex occlusion scenarios, allowing some NLOS satellites to retain excessively high weights. To address these limitations, this paper proposes conformal prediction (CP)-single point positioning (SPP), which integrates CP into GNSS satellite weighting. Using a gradient boosting decision tree as the base classifier, we construct a ten-dimensional feature vector from C/N0, elevation angle, pseudorange residuals, and related observables. Conformal p-values are computed for each satellite based on an LOS calibration set—lower values indicating higher NLOS likelihood—and mapped to continuous weights via an exponential function, effectively down-weighting NLOS satellites while preserving LOS satellite weights; all satellites are retained to maintain geometric strength. Evaluated on the Hong Kong UrbanNav dataset with 10% labeled target-domain samples, CP-SPP achieves a horizontal positioning RMSE of 10.74 m and a CEP of 4.77 m, representing improvements of 30.8% and 53.2% over traditional elevation-angle weighting and 14.6% and 27.8% over machine learning probability weighting. The CP framework attains a 97.1% LOS/NLOS prediction-set coverage rate (exceeding the 90% nominal target), with 90.0% of satellites receiving singleton LOS or NLOS prediction sets, demonstrating that CP offers a promising approach for reliable GNSS single-point positioning in complex urban environments.

GNSS Signal Diffraction Effects in High Precision Positioning.

High-precision GNSS is fundamental to modern geodesy. Standard processing assumes line-of-sight signal propagation, treating residual non-line-of-sight effects as multipath or random noise. This thesis shows that diffraction caused by signal bending around obstacles, is a distinct, deterministic error source that biases key geodetic parameters (coordinates, troposphere) in ways that averaging or double-differencing cannot remove. Unmodeled diffraction introduces slowly varying carrier-phase biases that affect station coordinates (especially the vertical component), hinder ambiguity resolution, and mimic tropospheric zenith delays. Under common field conditions (e.g., a 1 m obstacle at 1 m distance), biases can reach decimeter levels, leading to false interpretations of tectonic motion, seasonal deformation, or local subsidence. Because diffraction correlates with satellite geometry, it aliases into tropospheric estimates, degrading climate-related GNSS applications. The DOP metric alone is insufficient, and conventional multipath mitigation (choke rings, absorbers) is largely ineffective against diffraction. This thesis makes four novel contributions. First, it clearly distinguishes diffraction from multipath using GNSS SNR observables and carrier-phase residuals (from PPP and double differences), resolving a long-standing ambiguity. Second, a controlled movable-wall experiment quantifies the inverse distance dependence of diffraction error, validates knife-edge models at far-field (2 m) while revealing their near-field limitations (1 m), and derives an operational guideline (obstacle subtended angle <11°) for PPP and RTK. Third, a first-of-its-kind phasor-based, data-driven interference model for near-field cylindrical interference achieves correlations >0.61 and mm-level residuals, turning empirical site-calibration maps into interpretable physical models. Fourth, diffraction analysis is extended to tropospheric parameter estimation, uncovering previously undocumented errors in estimated zenith total delays and gradients. The thesis includes three introductory chapters (GNSS error sources, diffraction theory, post-processing software) and five appended papers. Together, they reclassify diffraction from a neglected phenomenon into a quantifiable, modelable one, with direct implications for monument design, site selection, and interpretation of long-term coordinate time series in high-precision geodesy.

DNN-Based 3D Relative Positioning Using Inter-Node Distances in Indoor Environments

In indoor environments, the accuracy of GPSbased positioning is significantly degraded by signal blockage, multipath propagation, and structural interference, making alternative approaches essential for precise indoor localization. This paper presents a deep neural network (DNN)-based threedimensional relative positioning method that relies solely on internode distance information. Experimental results show that the DNN-based method maintains more stable MAE performance as distance measurement errors increase and consistently achieves lower root mean squared error (RMSE) than the grid-based algorithm across all node configurations. In particular, as the distance measurement error grows, the grid-based algorithm exhibits pronounced performance degradation due to error accumulation during the grid-search process, whereas the DNN-based method shows more gradual degradation by learning the nonlinear relationship between distance information and relative coordinates. Furthermore, the results indicate improved scalability and robustness to distance measurement noise as the number of nodes increases. These findings suggest that the DNN-based approach has potential as an effective three-dimensional relative positioning solution for indoor node systems such as drone swarms and mobile robot networks.