Hankel and Toeplitz Rank-1 Decomposition of Arbitrary Matrices with Applications to Signal Direction-of-Arrival Estimation
Provides computationally efficient and theoretically optimal estimators for few-shot direction-of-arrival estimation, a key problem in autonomous systems.
This paper develops algorithms for optimal rank-1 Hankel and Toeplitz matrix decomposition under L2 and L1 norms, and derives maximum-likelihood optimal direction-of-arrival estimators for few-shot scenarios, validated via simulations and real-world data.
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.