A self-supervised training route recorded the lowest reported positioning-error score in the study’s Heavy OOD category, the label used for open-source urban-driving scenarios kept outside supervised training and validation. Called SSL+FNT, it scored 18.96, compared with 21.26 for the supervised-only SPRVO route and 28.76 for the initial WLS solution.
That lead did not hold across every test category. SSL+FNT also had the lowest score for ID data, 2.64, against 2.85 for SPRVO and 4.98 for WLS. In Slight OOD, however, SPRVO led with 7.28, compared with 7.72 for SSL+FNT and 9.16 for WLS.
The study’s accuracy measure is a single combined score: the average of the 50th and 95th percentiles of 3D positioning error. Lower scores indicate better reported positioning accuracy. Per-epoch errors were pooled across repeated runs with different random seeds before the percentiles were calculated, but no uncertainty intervals or significance tests were reported.
A training route that starts before labels
The paper asks whether JEPA-based self-supervised pretraining can produce lower GNSS PVT positioning-error scores and more reliable predictions under urban multipath than supervised-only training and an initial WLS solution. It compares a supervised-only route trained from scratch with an SSL+FNT route that uses pretraining followed by finetuning.
In DLE-PVT, a feature extractor forms token sequences from contextual features and multipath indicators. A Transformer then predicts a code correction and an uncertainty value for each token. The reported architecture has four encoder blocks and two decoder blocks, with four attention heads in each block, a 32-dimensional embedding, a 128-dimensional feed-forward layer and approximately 100,000 parameters.
For self-supervised learning, the system masks low-elevation tokens below 40 degrees inside a randomly selected azimuth sector covering 25% of the sky. It uses JEPA to predict in representation space and adds VICReg regularization. The supervised objective uses a reference multipath approximation and a heteroscedastic regression loss based on a Laplace likelihood to guide correction and uncertainty predictions together.
SPRVO is trained from scratch with the supervised objective. SSL+FNT first pretrains the encoder, then transfers and freezes it while retraining the decoder and prediction head.
A deliberately split test
The empirical material combines 24 hours of proprietary Toulouse driving with PPC and UrbanNav open-source scenarios. The report describes Circuit #1 as eight scenarios containing 1.35 million tokens, Circuit #2 as four scenarios with 600,000 tokens, and the remaining open-source scenarios as nine scenarios with 130,000 tokens.
Testing used a strict scenario-level split: scenarios used for supervised training and validation were excluded from the test set. Circuit #1 was treated as ID, Circuit #2 as Slight OOD, and the open-source data as Heavy OOD.
The first experiment used 1 million Circuit #1 tokens and five runs. A second experiment added 600,000 pretraining tokens, 150,000 finetuning tokens, or both; it also scaled the model to 500,000 parameters and used three runs for each configuration. SSL+FNT finetuning was performed once per pretrained model.
The data-diversity results point to a different trade-off depending on the category. Among four configurations, Mixed/Basis had the lowest Slight OOD score at 8.59, while Basis/Mixed had the lowest Heavy OOD score at 18.67. For ID, Basis/Basis and Mixed/Basis tied for the lowest reported score at 2.55, while Mixed/Mixed was highest at 2.68. The paper states that the two experiment tables use different test scenarios, so their scores should not be compared directly.
Signals in the predictions
The prediction diagnostics also differed between routes. The supervised-only correction prediction had a stronger correlation with the initial WLS SD code residual than SSL+FNT, 0.96 versus 0.91. By contrast, SSL+FNT’s uncertainty was meaningfully related to several features, while supervised-only uncertainty remained loosely correlated.
An attention analysis did not establish why the model performed as it did. In a randomly selected SSL+FNT model on UrbanNav, early encoder layers emphasized high elevation, later encoder layers emphasized low elevation, and the last decoder layer emphasized the current token’s azimuth sector.
The authors interpret the overall pattern as supervised learning supplying correction and uncertainty prediction, with self-supervised learning improving prediction coherence through higher-quality, robustly grounded representations. They hypothesize that, after modest additional labeled-data collection, scaling unlabeled pretraining alone could improve generalization. That proposed next step is a hypothesis, not a result of the reported experiments.
What the comparison can say
The evidence is confined to the named datasets and scenario categories, so the reported rankings are a descriptive comparison within this evaluation. The paper reports no uncertainty intervals or significance tests, and in the second experiment SSL+FNT finetuning was done once per pretrained model.
The document is an arXiv preprint, version 1 dated 26 August 2026. Its front matter also notes presentation at the European Navigation Conference 2026.
Paper data and sources
Original title: Opportunities of Self Supervised Learning for GNSS: Evaluation of a Deep Learning-Enhanced PVT Algorithm
Authors: Thomas Barbero, Bertrand Ekambi
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text