Physics-guided deep metric learning with continuous time embeddings for open-world radar pulse de-interleaving

Radar pulse de-interleaving is a foundational Electronic Support Measures (ESM) task that aims to separate chronologically interleaved pulse streams from multiple non-cooperative transmitters under unknown emitter cardinality in dense, contested electromagnetic environments. Classical histogram transforms and closed-world deep classifiers degrade under severe pulse loss, agile Pulse Repeti tion Interval (PRI) modulation, and spurious clutter. In this paper, we systematically characterise continuous temporal representations and physics-guided model selection in deep metric learning for open-world radar de-interleaving. Building on the transformer-based metric-learning framework for open-world deinterleaving introduced by Gunn et al. [1], we introduce a continuous Time-of-Arrival (ToA) sinusoidal positional encoding that directly models physical inter-pulse durations rather than ordinal token indices, a design choice that contrasts with [1], who found ordinal positional encodings provided no benefit and omitted them entirely. Neural network parameters are optimised solely via Supervised Contrastive (SupCon) learning, while scale-aware physical domain priors based on PRI Consistency and Angle-of-Arrival (AoA) continuity serve as physics-guided validation and checkpoint-selection criteria operating on unsupervised HDBSCAN cluster assignments.