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 $2\pi$ . 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.

中文翻译：

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稀疏线阵测向的实用丢番图近似


本文提出了一种计算高效、固定复杂度的算法，用于估计撞击稀疏线性传感器阵列的射频信号的到达角。方位估计问题的似然函数被简化为涉及 $2\pi$ 整数倍未知集合的非齐次丢番图近似问题。在求解整数时，我们提出了对 Cassels 算法的修改，并生成方位的近似线性化最大似然 (ML) 估计。算法收敛的迭代次数可以预先计算，这使得算法具有固定的计算复杂度。所提出的技术适用于一大类阵列配置，允许选择阵列配置来优化估计性能而不是适应算法。仿真结果表明，所提出的方位估计算法的性能非常接近 ML 估计的性能，但计算开销显着降低。