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

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.