PC-DeepNet: A GNSS Positioning Error Minimization Framework Using Permutation-Invariant Deep Neural Network

TL;DR

PC-DeepNet presents a permutation-invariant DNN framework to mitigate GNSS positioning errors in urban environments by learning a 3D position correction from a set of per-satellite features, including pseudorange residuals, LOS vectors, GDOP, $C/N_0$, and elevation. The encoder–aggregation–decoder PI-DNN handles variable satellite counts via sum-pooling, using a robust r-WLS initial guess and smooth L1 loss to train on ground-truth corrections. Evaluations on two public Android GNSS datasets show the approach achieves superior accuracy with lower computational footprint compared to state-of-the-art model-based and ML-based methods, across urban and suburban scenarios. The method is well-suited for resource-constrained IoT devices, with future work targeting additional GNSS constellations and broader geographic validation.

Abstract

Global navigation satellite systems (GNSS) face significant challenges in urban and sub-urban areas due to non-line-of-sight (NLOS) propagation, multipath effects, and low received power levels, resulting in highly non-linear and non-Gaussian measurement error distributions. In light of this, conventional model-based positioning approaches, which rely on Gaussian error approximations, struggle to achieve precise localization under these conditions. To overcome these challenges, we put forth a novel learning-based framework, PC-DeepNet, that employs a permutation-invariant (PI) deep neural network (DNN) to estimate position corrections (PC). This approach is designed to ensure robustness against changes in the number and/or order of visible satellite measurements, a common issue in GNSS systems, while leveraging NLOS and multipath indicators as features to enhance positioning accuracy in challenging urban and sub-urban environments. To validate the performance of the proposed framework, we compare the positioning error with state-of-the-art model-based and learning-based positioning methods using two publicly available datasets. The results confirm that proposed PC-DeepNet achieves superior accuracy than existing model-based and learning-based methods while exhibiting lower computational complexity compared to previous learning-based approaches.

Figures (14)

• Figure 1: The proposed PC-DeepNet to minimize the positioning error in NLOS and multipath environment.
• Figure 2: Proposed framework (PC-DeepNet) for positioning error minimization.
• Figure 3: Architecture of PI-DNN model to minimize the positioning error in NLOS and multipath environments.
• Figure 4: Test and train location map in San Francisco.
• Figure 5: Test and train location map in Los Angeles.