Optimal Temporal SNR Window for Multi-Sensor Fusion: Theory and Jamming-Aware GNN Architecture for Electronic Warfare

Multi-object tracking in electronic warfare (EW) relies heavily on temporal fusion - accumulating observations across frames through filtering or recurrent models. Yet this strategy relies on the premise that inter-frame data association is sufficiently accurate to benefit from accumulation. We challenge this assumption by analyzing the temporal signal-to-noise ratio SNRt=Δ p/σ (inter-frame displacement over measurement error) and deriving an Optimal SNR Window Theorem. Under nearest-neighbor association, temporal modeling is harmful when SNRt≲ 5%, beneficial between 5% and 45%, and saturated beyond; these boundaries are operating-region markers under the assumed association model. In EW scenarios with heavy jamming and false-target injection, SNRt can fall to ∼2.3% - well inside the harmful region. We therefore design a single-frame graph attention network (GAT) with jamming-aware gating that bypasses temporal association entirely. On a multi-sensor benchmark (900 frames, 37.5% jammer ratio, 1200 injected false targets), the proposed method achieves OSPA of 2717± 449 and MOTA of 14.0%± 9.3% across seven seeds, outperforming both classical filters (JPDA, LMB/GLMB) and all temporal GNN variants, which produce negative MOTA. A sweep across six noise levels confirms the predicted non-monotonic benefit curve, peaking at SNRt=11.5% with negative gain at the 2.3% operating point.