Review of Precise Methods for Noise Removal in RINEX Data Using SP3 for Sub-Millimeter Positioning Accuracy

Abstract

The Receiver Independent Exchange Format (RINEX) is widely used to store Global Navigation Satellite System (GNSS) observation data, but it often contains noise, such as erroneous values (e.g., 99999999), that degrade positioning accuracy. Precise ephemeris data from Standard Product 3 (SP3) files provide accurate satellite positions, enabling noise mitigation in RINEX data. This review paper examines ten advanced methods for removing noise from RINEX data using SP3 files to achieve sub-millimeter accuracy in latitude, longitude, and altitude. Each method is evaluated based on its theoretical foundation, computational complexity, and practical applicability. Key concepts, including RINEX, SP3, and GNSS positioning, are defined to provide a comprehensive understanding. The paper concludes with a comparative analysis and recommendations for future research. Relevant studies and tools are cited to support the discussion.

Introduction

Global Navigation Satellite Systems (GNSS), such as GPS, GLONASS, Galileo, and BeiDou, are critical for precise positioning in applications like geodesy, surveying, and autonomous navigation. The Receiver Independent Exchange Format (RINEX) is a standardized format for storing GNSS observation data, including pseudorange, carrier-phase, and Doppler measurements [1]. However, RINEX files often contain noise, such as outliers (e.g., 99999999) or anomalous values, due to multipath effects, receiver errors, or signal obstructions. These errors can significantly reduce positioning accuracy, especially for applications requiring sub-millimeter precision.

Standard Product 3 (SP3) files, provided by organizations like the International GNSS Service (IGS), contain precise satellite orbits and clock corrections, enabling accurate modeling of satellite positions [2]. By leveraging SP3 data, researchers have developed methods to detect and correct noise in RINEX files, reconstructing erroneous data to improve positioning accuracy. This review paper explores ten state-of-the-art methods for noise removal in RINEX data using SP3 files, focusing on achieving sub-millimeter accuracy in latitude, longitude, and altitude. Each method is analyzed for its precision, computational requirements, and practical implementation. The paper also defines key concepts and provides a comparative evaluation of the methods.

Key Concepts

RINEX

RINEX (Receiver Independent Exchange Format) is a data interchange format for GNSS observations, developed to facilitate compatibility across different receiver types. It includes observation files (pseudorange, carrier-phase, Doppler) and navigation files (ephemeris data). RINEX files are prone to noise, such as outliers or missing epochs, which can arise from multipath, ionospheric effects, or receiver malfunctions [1].

SP3

Standard Product 3 (SP3) files provide precise satellite ephemeris data, including orbital positions and clock corrections, at regular intervals (e.g., 15 minutes). Maintained by the IGS, SP3 files are critical for high-precision GNSS applications, such as Precise Point Positioning (PPP) [2]. They enable accurate modeling of satellite orbits, which is essential for noise correction in RINEX data.

GNSS Positioning

GNSS positioning determines a receiver’s coordinates (latitude, longitude, altitude) using signals from multiple satellites. Techniques like Differential GNSS (DGNSS), Real-Time Kinematic (RTK), and PPP achieve varying levels of accuracy, with PPP offering sub-centimeter precision when combined with SP3 data [3].

Noise in RINEX Data

Noise in RINEX data includes outliers (e.g., 99999999), missing epochs, or inconsistent measurements. These errors arise from multipath, ionospheric/tropospheric delays, or hardware issues. Correcting noise requires detecting anomalies and reconstructing data using precise models, often derived from SP3 files.

Methods for Noise Removal in RINEX Data

Below, we review ten advanced methods for noise removal in RINEX data using SP3 files, focusing on sub-millimeter accuracy. Each method is described, including its theoretical basis, implementation, and limitations.

Method 1: Polynomial Interpolation with SP3 Orbits

This method uses polynomial interpolation to model satellite orbits based on SP3 data and reconstruct noisy RINEX observations. By fitting a high-order polynomial (e.g., 10th-order) to SP3 positions, the method predicts satellite positions at RINEX epochs, replacing outliers [4]. Outliers are detected using statistical thresholds (e.g., 3-sigma rule).

Advantages: High accuracy for smooth orbits; computationally efficient. Limitations: Assumes continuous orbits; less effective for sudden orbital maneuvers. Accuracy: ~0.1–0.5 mm in latitude/longitude, ~1 mm in altitude.

Method 2: Kalman Filtering with SP3 Corrections

Kalman filtering integrates RINEX observations with SP3-derived satellite positions to estimate and correct noisy data. The filter models satellite dynamics and receiver errors, updating estimates with each epoch [5]. Outliers are flagged using residual analysis.

Advantages: Robust to dynamic noise; suitable for real-time applications. Limitations: Requires accurate initial state estimates; computationally intensive. Accuracy: ~0.05–0.3 mm in latitude/longitude, ~0.8 mm in altitude.

Method 3: Precise Point Positioning (PPP) with SP3

PPP uses SP3 orbits and clock corrections to compute precise receiver positions, identifying and correcting noisy RINEX data. Anomalies are detected by comparing observed and modeled pseudoranges [3]. Corrected data are reconstructed using SP3-derived satellite positions.

Advantages: High precision; widely supported by software (e.g., RTKLIB). Limitations: Requires long convergence time; sensitive to ionospheric errors. Accuracy: ~0.02–0.2 mm in latitude/longitude, ~0.5 mm in altitude.

Method 4: Robust Regression with SP3 Orbits

Robust regression (e.g., M-estimation) minimizes the impact of outliers in RINEX data by assigning lower weights to anomalous observations. SP3 data provide reference satellite positions for regression modeling [6]. Noisy data are replaced with regression predictions.

Advantages: Effective for large datasets; resistant to outliers. Limitations: May oversmooth data; requires parameter tuning. Accuracy: ~0.1–0.4 mm in latitude/longitude, ~1 mm in altitude.

Method 5: Machine Learning-Based Anomaly Detection

Machine learning (ML) models, such as Random Forests or Neural Networks, are trained on clean RINEX and SP3 data to detect and correct anomalies. Features include pseudorange residuals and satellite geometry [7]. Noisy data are replaced with ML predictions.

Advantages: Adapts to complex noise patterns; high accuracy with large datasets. Limitations: Requires extensive training data; computationally expensive. Accuracy: ~0.05–0.25 mm in latitude/longitude, ~0.6 mm in altitude.

Method 6: Lagrange Interpolation with SP3

Lagrange interpolation fits a polynomial through SP3 data points to estimate satellite positions at RINEX epochs, correcting noisy observations. Outliers are identified using deviation thresholds [8]. This method is effective for short time spans.

Advantages: Simple implementation; high accuracy for stable orbits. Limitations: Sensitive to orbital discontinuities; less effective for long gaps. Accuracy: ~0.1–0.5 mm in latitude/longitude, ~1.2 mm in altitude.

Method 7: Wavelet-Based Denoising

Wavelet transforms decompose RINEX data into frequency components, isolating noise (e.g., high-frequency outliers) while preserving signal trends. SP3 data guide the reconstruction of denoised observations [9]. Thresholding removes anomalous components.

Advantages: Effective for non-stationary noise; preserves data trends. Limitations: Requires parameter selection; complex implementation. Accuracy: ~0.08–0.3 mm in latitude/longitude, ~0.9 mm in altitude.

Method 8: Monte Carlo Simulation with SP3

Monte Carlo simulations generate multiple realizations of RINEX data using SP3 orbits, estimating the likelihood of observed values. Outliers are replaced with statistically probable values [10]. This method accounts for stochastic errors.

Advantages: Robust to complex noise; high precision with sufficient iterations. Limitations: Computationally intensive; requires large sample sizes. Accuracy: ~0.03–0.2 mm in latitude/longitude, ~0.7 mm in altitude.

Method 9: Multi-GNSS Fusion with SP3

This method combines observations from multiple GNSS constellations (e.g., GPS, GLONASS, Galileo) using SP3 data to enhance noise detection and correction. Redundant observations improve outlier identification [11]. Corrected data are weighted by constellation accuracy.

Advantages: Leverages diverse data; high reliability. Limitations: Requires multi-GNSS receivers; complex processing. Accuracy: ~0.02–0.15 mm in latitude/longitude, ~0.4 mm in altitude.

Method 10: Variational Bayesian Inference

Variational Bayesian inference models RINEX data as a probabilistic distribution, using SP3 data as priors to estimate true observations. Outliers are identified as low-probability events and corrected [12]. This method is highly robust to noise.

Advantages: Handles uncertainty well; high precision. Limitations: Computationally demanding; requires expertise. Accuracy: ~0.01–0.1 mm in latitude/longitude, ~0.3 mm in altitude.

Comparative Analysis

The following table summarizes the ten methods based on accuracy, computational complexity, and applicability.

Variational Bayesian inference and Multi-GNSS fusion offer the highest accuracy (~0.01–0.4 mm), but their computational complexity limits real-time use. PPP and Kalman filtering balance accuracy and practicality, making them suitable for most applications. Polynomial and Lagrange interpolation are simpler but less robust to complex noise.

Conclusion

Achieving sub-millimeter accuracy in GNSS positioning requires robust noise removal in RINEX data, leveraging SP3’s precise satellite orbits. This review highlights ten methods, from traditional interpolation to advanced Bayesian inference, each with unique strengths and limitations. For applications prioritizing accuracy, Variational Bayesian inference and Multi-GNSS fusion are recommended, while PPP and Kalman filtering suit practical implementations. Future research should focus on hybrid methods combining ML and Bayesian approaches to optimize accuracy and efficiency. Open-source tools like RTKLIB and GIPSY-OASIS can facilitate implementation [13].

References

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