A Complex Hermitian Positive Definite Manifold Embedding Transformer Network for Time-Varying Direction of Arrival Tracking

In this work, we address the challenge of stable and robust time-varying direction-of-arrival (DOA) tracking, where both the DOA trajectory and the number of sources change over time across different scenarios. We formulate the problem as a multi-label classification task and propose a novel solution leveraging Riemannian manifold geometry and advanced neural networks for sequential data processing. Specifically, we introduce the Complex Hermitian Positive Definite embedding Transformer (C-HPD-T) network, which learns statistical representations of covariance matrices. The C-HPD-T consists of an HPD module and a Transformer module. The HPD module learns an appropriate statistical representation and the complex Transformer module models the data temporally. In particular, in the C-HPD-T network, we build a complex singular value decomposition (SVD) module to ensure that complex structure is preserved during the calculation of each layer. Meanwhile, we design a Transformer-based sequential network to capture the temporal relationship of signals and for the time-varying DOAs. Through training the network with varying numbers of moving targets featuring diverse motion trajectories, the network demonstrates excellent performance and robustness against array imperfections. Extensive simulation results demonstrate its superior performance gains compared to existing methods.