Direct Position Determination of Coherently Distributed Sources based on Compressed Sensing with a Moving Nested Array

Abstract

The existing direct position determinations(DPD) for coherently distributed(CD) sources are mostly applicable for uniform linear array(ULA), which result in a low degree of freedom(DOF), and it is difficult for them to realize the effective positioning in underdetermined condition. In this paper, a novel DPD algorithm for coherently distributed sources based on compressed sensing with a moving nested array is present. In this algorithm, the nested array is introduced to DPD firstly, and a positioning model of signal moving station based on nested array is constructed. Owing to the features of coherently distributed sources, the cost function of compressed sensing is established based on vectorization. For the sake of convenience, unconstrained transformation and convex transformation of cost functions are carried out. Finally, the position coordinates of the distribution source signals are obtained according to the theory of optimization. At the same time, the complexity is analyzed, and the simulation results show that, in comparison with two-step positioning algorithms and subspace-based algorithms, the proposed algorithm effectively solves the positioning problem in underdetermined condition with the same physical element number.