Towards End-to-End GPS Localization with Neural Pseudorange Correction

TL;DR

This work tackles GPS localization accuracy bottlenecks caused by pseudorange errors by proposing E2E-PrNet, an end-to-end framework that learns a neural pseudorange correction (PrNet) and feeds corrected measurements into a differentiable nonlinear least squares (DNLS) optimizer. Training uses the final task loss, propagating gradients through the unrolled Gauss-Newton iterations to adjust PrNet parameters, and it supervises clock offsets via WLS labels to address missing-label issues. Experiments on the Google Smartphone Decimeter Challenge show E2E-PrNet outperforms a baseline WLS method and a leading end-to-end approach, with notable improvements in horizontal positioning under fingerprinting and cross-trace scenarios, and analyses confirm the front-end PrNet learns to approximate smoothed pseudorange errors. The approach demonstrates a principled fusion of data-driven correction with model-based optimization, offering practical gains for smartphone GNSS localization and a path toward extending to additional constellations and measurements.

Abstract

The pseudorange error is one of the root causes of localization inaccuracy in GPS. Previous data-driven methods regress and eliminate pseudorange errors using handcrafted intermediate labels. Unlike them, we propose an end-to-end GPS localization framework, E2E-PrNet, to train a neural network for pseudorange correction (PrNet) directly using the final task loss calculated with the ground truth of GPS receiver states. The gradients of the loss with respect to learnable parameters are backpropagated through a Differentiable Nonlinear Least Squares (DNLS) optimizer to PrNet. The feasibility of fusing the data-driven neural network and the model-based DNLS module is verified with GPS data collected by Android phones, showing that E2E-PrNet outperforms the baseline weighted least squares method and the state-of-the-art end-to-end data-driven approach. Finally, we discuss the explainability of E2E-PrNet.

Figures (9)

• Figure 1: An overview of our E2E-PrNet GPS localization pipeline. The learnable parameters $\boldsymbol{\upphi}$ of the neural network for pseudorange correction are tuned by the final task loss calculated using the receiver states $\mathbf{X}^*$.
• Figure 2: The diagram of PrNet. PrNet consists of a MLP layer for pseudorange error regression and a mask layer for filtering out visible satellites. $B$ represents the batch size. $F$ denotes the feature dimension. $H$ is the number of hidden neurons.
• Figure 3: The computational graph of the unrolling Gauss-Newton iteration: the forward process (in blue lines) and the backward process (in green dash lines)
• Figure 4: (a) Scenario I: fingerprinting. (b) Scenario II: cross trace.
• Figure 5: Horizontal errors in (a) Scenario I. (b) Scenario II.