Bayesian Jammer Localization with a Hybrid CNN and Path-Loss Mixture of Experts

Global Navigation Satellite System (GNSS) signals are vulnerable to jamming, particularly in urban areas where multipath and shadowing distort received power. Previous data-driven approaches achieved reasonable localization but poorly reconstructed the received signal strength (RSS) field due to limited spatial context. We propose a hybrid Bayesian mixture-of-experts framework that fuses a physical path-loss (PL) model and a convolutional neural network (CNN) through log-linear pooling. The PL expert ensures physical consistency, while the CNN leverages building-height maps to capture urban propagation effects. Bayesian inference with Laplace approximation provides posterior uncertainty over both the jammer position and RSS field. Experiments on urban ray-tracing data show that localization accuracy improves and uncertainty decreases with more training points, while uncertainty concentrates near the jammer and along urban canyons where propagation is most sensitive.