Direct Position Determination via Joint Sparse Representation of Array Covariance Matrices Based on Angle and Doppler

Bycontrast with the two-step localization method, which requires estimation of intermediate positions, the direct position determination (DPD) method locates the source directly from the received signal and has better localization performance at low signal-to-noise ratios (SNRs). This article proposes a DPD method based on a joint sparse representation of angle and Doppler information for a single moving observation station. It exploits the inherent sparsity of sources in the spatial domain and transforms the localization problem into a sparse reconstruction problem. As a result of the conjunction of angle and Doppler frequency shift, the observation signal is constructed, and a joint sparse representation of array covariance matrices is used to obtain the localization model. The source position is also reconstructed using the reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{l}_{1}}$</tex-math></inline-formula>-norm convex optimization method. This algorithm provides better and more stable localization performance with limited SNR and number of snapshots. In addition, it is suitable for environments involving adjacent sources. Simulations are performed to evaluate the effectiveness of the proposed algorithm.