Enhancing D-Band FMCW Radar Tracking for In-Air Writing Through Weakly Supervised Deep Association

Reconstructing precise character trajectories in multipath environments represents a primary challenge for high-fidelity reconstruction for radar-based in-air writing. Existing tracking methods typically rely on dominant target assumptions, often failing to account for the interference of multipath reflections. Conversely, end-to-end deep learning approaches generally lack the physical interpretability necessary for accurate geometric drawing. In this work, we propose a novel tracking framework that combines high-resolution D-band sensing with a data-driven probabilistic data association (PDA) architecture. We leverage a 56 GHz bandwidth FMCW radar setup to capture fine-grained kinematic signatures, supported by a rigorous sensor placement and calibration strategy. To address multipath interference without relying on rigid parametric assumptions, we propose the Temporal Deep PDA (TD-PDA). This architecture replaces heuristic hard-assignments and classical parametric clutter models with a covariance-aware causal Temporal Convolutional Network fused directly into the statistical covariance spread equations of an Extended Kalman Filter. To train the network without heuristic bias, we introduce a Track Quality Indicator ensemble to automatically extract high-fidelity pseudo-labels. The framework is rigorously validated via simulated ground-truth data to quantify the geometric impacts of hardware constraints, and experimentally proven on a 1000-gesture dataset using 10-Fold Leave-One-Subject-Out cross-validation. The proposed TD-PDA generalizes to unseen users with an ultra-low inference latency, successfully reconstructing legible trajectories even in the presence of strong multipath interference. The model demonstrates improvements over prior deep-association architectures and achieves stability comparable to a well-tuned classical PDA filter via a purely data-driven design.