Geometric Direction Finding on Dynamic Manifolds: Unambiguous DOA Estimation for Spatially Undersampled UWB Arrays

Traditional Direction of Arrival (DOA) estimation methods struggle to simultaneously address three physical constraints in Ultra-Wideband (UWB) electromagnetic sensing: spatial undersampling, asynchronous array phase, and beam squint. Existing solutions treat these issues in isolation, leading to limited performance in complex scenarios. This paper proposes a novel dynamic manifold perspective, which models UWB signal observations as a continuous manifold curve in a high-dimensional space driven by temporal evolution and array topology. We theoretically demonstrate that the DOA can be uniquely determined solely by the geometric shape of the manifold, rather than the absolute arrival phase. Based on this perspective, we construct a geometric parameter system comprising extrinsic and intrinsic parameters, along with a corresponding DOA estimation framework. Extrinsic vector parameters serve as a dynamic extension of traditional array processing, effectively expanding the degrees of freedom to suppress grating lobes. Intrinsic scalar invariants provide a new geometric perspective independent of traditional phase models, offering intrinsic robustness against array channel phase errors. Simulation results show that the derived analytical expressions for geometric parameters are highly consistent with numerical truths. The proposed framework not only completely eliminates spatial ambiguity in sparse arrays but also achieves high-precision direction finding under conditions with calibration-free phase errors.