High-Frequency Skywave Source Geolocation Using Deep Learning-Based TDOA Estimation and Bias-Regularized Semidefinite Programming with Field Evaluation

High-frequency (HF) skywave propagation exploits ionospheric reflection for beyond-line-of-sight transmission, making time-difference-of-arrival (TDOA)-based geolocation a primary technique for localizing non-cooperative HF emitters. However, reliable TDOA estimation remains challenging due to time-varying ionospheric conditions, wideband multipath dispersion, and low signal-to-noise ratio (SNR). This paper proposes an integrated framework coupling realistic channel synthesis, deep learning-based TDOA estimation, and convex optimization-based localization. Three contributions are made. First, an improved wideband ionospheric channel model is constructed by integrating the International Reference Ionosphere (IRI) with region-specific calibration and a stochastic perturbation module, yielding time-varying multipath responses for physics-consistent waveform generation. Second, a convolutional neural network (CNN)-based TDOA estimator is designed to jointly exploit time-domain complex-baseband in-phase/quadrature (I/Q) waveforms, multi-weight generalized cross-correlation (GCC) feature maps, and channel-state information (CSI) within a unified regression network, achieving robust delay estimation under severe noise and multipath conditions. Third, the geolocation problem is formulated as a bias-regularized constrained least-squares problem with unknown ionospheric excess-delay surrogates, and a semidefinite programming (SDP) relaxation is derived to yield a tractable solution without prescribing a fixed virtual reflection height. Simulations show that the proposed estimator consistently outperforms competing algorithms across a wide SNR range and narrows the gap to the Cramér–Rao lower bound (CRLB) at high SNR. On field-recorded signals, the estimator reduces the mean absolute TDOA deviation by 51% relative to GCC with phase transform (GCC-PHAT), and the end-to-end pipeline achieves a mean geolocation error of 19.67 km across 100 field segments, outperforming all compared baselines.