Real-time DOA Estimation for Mission-critical Military Asset Tracking Using Quaternion-valued Signal Models for Risk Reduction

Accurate, low-latency direction-of-arrival (DoA) estimation is pivotal for tracking mission-critical assets in contested environments. This work introduces a constraint-aware quaternion MUSIC framework (QMUSIC++) that jointly exploits spatial and polarization diversity while explicitly budgeting for latency, robustness, and scalability. The method combines (i) quaternion-domain covariance estimation with shrinkage for low-SNR and jamming resilience, (ii) a Cayley–Dickson adjoint eigen-decomposition for computational tractability, (iii) polarization-aware steering vectors, and (iv) a penalty-augmented pseudospectrum that suppresses jammer-induced spurious lobes and enforces processing-time limits. Simulations show consistently higher resolution probability and lower RMSE than classical MUSIC/ESPRIT and long-vector/scalar baselines, particularly at low to moderate SNR; accuracy remains close to the Cramer–Rao bound. Complexity profiling indicates real-time feasibility on embedded ARM class hardware (sub-10 ms per snapshot for representative grid sizes), with desktop throughput in the hundreds of snapshots per second. The results support quaternion-valued processing as a compact, robust, and deployable solution for real-time asset tracking and risk reduction in defence settings. The validation was conducted on synthetic benchmark datasets generated using a dual-polarised uniform linear array (ULA) model under varying SNR and jamming conditions to emulate real embedded operations.