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

TL;DR

The paper tackles GNSS jammer localization and RSS-field reconstruction in urban settings where multipath and shadowing distort signals. It introduces a hybrid Bayesian mixture-of-experts that fuses a physical path-loss model with a CNN using log-linear pooling, yielding a joint posterior over the jammer position $\boldsymbol \theta$ and the RSS field via a Laplace approximation. Key contributions include explicit probabilistic modeling of both the jammer location and the propagation field, a data-driven prior on $\boldsymbol\theta$, and predictive distributions that decompose uncertainty into aleatoric and epistemic components. Experiments on urban ray-tracing data show that localization accuracy improves with more training data and that uncertainty concentrates near the jammer and urban canyons, highlighting the framework’s potential for uncertainty-aware active learning and interference mitigation.

Abstract

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.

Figures (4)

• Figure 1: CNN expert architecture. The input $\mathbf{X}\in\mathbb R^{3\times H\times W}$ combines building heights and spatial coordinates. The network consists of convolutional layers with batch normalization and ReLU, with dropout regularization, followed by a final convolution and global average pooling to produce an $H\times W$ RSS field prediction.
• Figure 2: Simulated jammer RSS field for downtown Chicago. Urban canyon effects create higher power along aligned streets, while building shadows cause attenuation.
• Figure 3: Five-panel visualization of jammer localization experiments. From left to right: (1) Simulated RSS field with 200 training points overlaid; (2) Path-loss expert prediction $\mu^{\mathrm{PL}}(\mathbf p; \hat{\boldsymbol \psi}_{\mathrm{MAP}_{\boldsymbol \theta,P_0,\gamma}})$; (3) CNN expert prediction $\mu^{\mathrm{CNN}}(\mathbf p; \mathbf X,\hat{\boldsymbol \psi}_{\mathrm{MAP}_{\boldsymbol \omega}})$; (4) Pooled mean $\mu(\mathbf p;\mathbf{H}_{\text{bld}},\hat{\boldsymbol \psi}_{\mathrm{MAP}})$ (equals the mean of the predictive distribution under the Laplace approximation of the posterior); and (5) Pooled predictive uncertainty (standard deviation). All panels include the building layout in the background and markers for the true jammer position (red star) and predicted position (white star). Panels (1)--(4) share a common RSS colorbar, while panel (5) uses a separate uncertainty scale.
• Figure 4: Performance versus training set size (20–500 points), averaged over 50 Monte Carlo runs. Top: Jammer localization error (m) and posterior std. dev. (m). Bottom: RSS field test RMSE (dBW) and field test RMPV (dBW).