SGprAle: Self-supervised Gaussian process regression for average localisation error estimation in wireless Nnetworks

This paper presents sGprAle, a self-supervised framework for predicting Average Localisation Error (ALE) in wireless sensor networks under limited labeled data conditions. The proposed approach integrates Gaussian Process Regression (GPR) with an autoencoder-based feature learning strategy to enhance robustness, generalisation, and predictive reliability. By learning task-agnostic latent representations from unlabeled data through a reconstruction objective, sGprAle enables the GPR model to operate in a compact and informative latent space using only a small labeled subset. Bayesian optimisation is employed to adapt kernel hyperparameters, ensuring calibrated uncertainty estimates and stable performance when labeled data are scarce. The framework is systematically evaluated across multiple labeled-data scenarios using ablation studies, uncertainty analysis, and statistical comparisons. Results demonstrate that the self-supervised latent representation substantially improves model robustness and label efficiency, allowing sGprAle to achieve competitive accuracy relative to existing methods while requiring significantly fewer labeled samples. These findings highlight the effectiveness of combining self-supervised representation learning with probabilistic regression for addressing the node localisation problem. The proposed model offers a reliable and energy efficient solution for ALE prediction, contributing to improved localisation performance and operational efficiency in wireless sensor networks.