A Practical Diophantine Approximation for Sparse Linear Array Direction Finding

• Published in: IEEE transactions on aerospace and electronic systems Vol. 57; no. 3; pp. 1405 - 1412
• Main Authors: Sirianunpiboon, Songsri, Ly, Peter Q. C., Elton, Stephen D.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Ambiguity resolution; Angle of arrival; angle of arrival estimation; Approximation; Approximation algorithms; Cassels algorithm; Complexity; Configurations; Davenport algorithm; Diophantine approximation; Direction finding; interferometry; Linear antenna arrays; Linear arrays; linearized maximum likelihood (ML); Mathematical analysis; Mathematical model; Maximum likelihood estimates; Maximum likelihood estimation; Phased arrays; Radio signals; Sensor arrays; Sensors; sparse antenna array
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2020.3046080

This article presents a computationally efficient, fixed complexity algorithm for estimating the angle of arrival of a radio frequency signal that impinges on a sparse linear array of sensors. The likelihood function for the bearing estimation problem is reduced to an inhomogeneous Diophantine approximation problem involving an unknown set of integer multiples of <inline-formula><tex-math notation="LaTeX">2\pi</tex-math></inline-formula>. In solving for the integers, we propose a modification to the Cassels algorithm and generate an approximate linearized maximum-likelihood (ML) estimate of bearing. The number of iterations for convergence of the algorithm can be precomputed, which allows the algorithm to have fixed computational complexity. The proposed technique applies to a large class of array configurations, allowing the array configuration to be chosen to optimize estimation performance rather than to suit the algorithm. The simulation results show the performance of the proposed bearing estimation algorithm to be very close to that of ML estimation, but with a significantly reduced computational overhead.