Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition

We consider the problems of computing the optimal rank-$1$ Hankel and Toeplitz-structured approximation of arbitrary matrices under $L_2$ and $L_1$-norm error. Such problems arise naturally in engineered systems, including the basic few-shot signal Direction-of-Arrival (DoA) estimation problem that is of importance to modern autonomous systems applications. We develop accurate and computationally efficient structured matrix decomposition algorithms for both formulations and then derive analytically grounded small-sample-support DoA estimators for practical sensing system deployments. The resulting estimators under the $L_2$ and $L_1$ norms are formally shown to be maximum-likelihood optimal under white Gaussian and Laplace noise, respectively. The estimators are further validated through extensive simulation studies and real-world data experiments in few-shot DoA inference.

Subspace methods such as multiple signal classification (MUSIC) achieve super-resolution direction of arrival (DoA) estimation by exploiting the orthogonality between the array manifold and the noise subspace of the measurements. Their accuracy therefore depends on the assumed manifold and degrades under model mismatch, while parameters not identifiable from the spatial manifold cannot be recovered. In this work, we propose the conditional neural manifold (CNM), which replaces the fixed manifold with an observation-conditioned mapping from source parameters to steering vectors. An encoder maps the snapshots to a latent scene representation that conditions a zero-initialized neural field over the parameter space. The manifold is learned without steering-vector supervision by shaping the resulting MUSIC landscape. Since the correction acts on the manifold rather than on the estimator, it can be used by other manifold-based methods without modification. The CNM restores resolution under array imperfections, colored noise, correlated sources, and near-field propagation, and resolves the angle-frequency ambiguity inherent to the nominal spatial manifold.

Direction-of-arrival (DOA) estimation is an important task in microphone array processing and many downstream applications. The steered response power with phase transform (SRP-PHAT) method has been widely adopted for DOA estimation in recent years. However, accurate SRP-PHAT estimation in 3D scenarios requires evaluating steering responses over thousands of candidate directions, severely limiting real-time performance on resource-constrained platforms. This challenge becomes even more critical for planar arrays, which are widely used in robotics due to their structural simplicity. Motivated by the fact that azimuth estimation is usually more reliable than elevation estimation for most arrays, we propose ASAP, an azimuth-priority strip-based search approach to planar microphone array DOA estimation in 3D. In the first stage, ASAP performs coarse-to-fine region contraction within azimuthal strips to lock azimuth angles while retaining multiple maxima through spherical caps. In the second stage, it refines elevation along the great-circle arc between two close candidates. Extensive simulations and real-world experiments validate the efficiency and merits of the proposed method over existing approaches.