[Paper Review] Robust Gaussian Process Regression for Real-Time High Precision GPS Signal Enhancement

Ming Lin, Xiaomin Song+5 more|arXiv (Cornell University)|Jun 3, 2019

Target Tracking and Data Fusion in Sensor Networks21 references4 citations

TL;DR

This paper proposes a three-step Filter-Reweight-Retrain (FRR) Gaussian Process regression method to enhance real-time GPS signal precision by robustly handling high levels of noise in ionospheric Total Electron Content (vTEC) data. By filtering outliers, reweighting residual errors, and retraining on both clean and reweighted noisy data, FRR achieves 78.4% centimeter-level positioning accuracy—outperforming state-of-the-art methods by 8.3% in benchmark tests despite a 30% outlier rate.

ABSTRACT

Satellite-based positioning system such as GPS often suffers from large amount of noise that degrades the positioning accuracy dramatically especially in real-time applications. In this work, we consider a data-mining approach to enhance the GPS signal. We build a large-scale high precision GPS receiver grid system to collect real-time GPS signals for training. The Gaussian Process (GP) regression is chosen to model the vertical Total Electron Content (vTEC) distribution of the ionosphere of the Earth. Our experiments show that the noise in the real-time GPS signals often exceeds the breakdown point of the conventional robust regression methods resulting in sub-optimal system performance. We propose a three-step approach to address this challenge. In the first step we perform a set of signal validity tests to separate the signals into clean and dirty groups. In the second step, we train an initial model on the clean signals and then reweigting the dirty signals based on the residual error. A final model is retrained on both the clean signals and the reweighted dirty signals. In the theoretical analysis, we prove that the proposed three-step approach is able to tolerate much higher noise level than the vanilla robust regression methods if two reweighting rules are followed. We validate the superiority of the proposed method in our real-time high precision positioning system against several popular state-of-the-art robust regression methods. Our method achieves centimeter positioning accuracy in the benchmark region with probability $78.4\%$ , outperforming the second best baseline method by a margin of $8.3\%$. The benchmark takes 6 hours on 20,000 CPU cores or 14 years on a single CPU.

Motivation & Objective

• To address the challenge of high noise corruption in real-time GPS signals, which degrades positioning accuracy below centimeter-level requirements.
• To develop a robust regression method capable of tolerating high outlier rates (up to 40%) in GPS data, where conventional robust methods fail.
• To improve model performance by leveraging both clean and noisy GPS data without discarding valuable high-precision measurements.
• To design a consistent and efficient algorithm that maintains accuracy even when the noisy dataset is infinite or heavily corrupted.
• To validate the superiority of the proposed FRR method over existing robust regression baselines in a real-world, large-scale GPS positioning system.

Proposed method

• The method begins by applying signal validity tests to classify GPS data into clean and dirty (noisy) groups.
• An initial Gaussian Process model is trained exclusively on the clean dataset to estimate vTEC values.
• The trained model predicts vTEC on the dirty dataset, and residual errors are computed to identify high-error points.
• Data points with large residuals are filtered out, while the remaining noisy points are reweighted based on their residual magnitude using a tuning parameter.
• A final robust GP model is retrained on the union of the clean dataset and the reweighted noisy dataset to improve generalization and accuracy.
• The reweighting scheme is designed to reduce variance in heavy-tailed noise, ensuring consistency even with infinite noisy data.

Experimental results

Research questions

• RQ1 Can a robust regression method handle GPS signal noise levels exceeding the breakdown point of conventional robust estimators?
• RQ2 How can valuable high-precision GPS data be preserved and effectively utilized when a significant portion is marked as noisy by an unreliable screening algorithm?
• RQ3 Does a three-step filtering, reweighting, and retraining strategy lead to consistent and improved model performance compared to iterative reweighting methods?
• RQ4 To what extent can the proposed FRR method outperform state-of-the-art robust regression techniques under high corruption rates in real-time GPS applications?
• RQ5 What is the theoretical guarantee of consistency and breakdown point convergence for the proposed FRR framework?

Key findings

• The proposed FRR method achieves a 78.4% RTK ratio for centimeter-level positioning accuracy in the benchmark region, significantly outperforming the second-best baseline by 8.3 percentage points.
• Even with up to 40% of data marked as noisy—especially during peak hours—FRR maintains high accuracy, avoiding service interruption.
• Conventional robust methods like Huber regression and IRLS fail under high corruption, with IRLS achieving less than half the RTK ratio of FRR.
• RANSAC performs poorly due to limited trial constraints in online systems, achieving an RTK ratio barely above 50%.
• Hard Iterative Thresholding (HIT) performs best among baselines but still fails under 30% noise, indicating limitations of existing methods in real-world high-noise GPS environments.
• Theoretical analysis confirms that FRR is consistent and achieves asymptotic breakdown point convergence to 1, making it uniquely suited for high-noise GPS signal processing.