Decoupled Message Passing Approach for Exact Mixed-Field Sources Localization

Mixed-field sources localization involves the simultaneous resolution of far-field (FF) and near-field (NF) sources, posing challenges due to the nonlinearity of NF steering and the additive coupling effect between these two types of sources. Current methods usually seek to linearize NF steering vectors using the Fresnel approximation and then employ a multistep strategy to independently localize FF and NF sources. However, both the Fresnel approximation and the multistep strategy can lead to significant performance degradation. To address these limitations, in this article, we propose a new decoupled message passing approach for exact mixed-field sources localization. Our method directly formulates the exact mixed-field sources localization as a multivariable sparse learning task and systematically addresses model mismatch under the Bayesian framework. Considering the time-consuming nature of multivariable Bayesian inference, we further introduce a novel auxiliary variable into the Bayesian framework. Subsequently, we devise an efficient decoupled message passing method to automatically separate the NF and FF signals, resulting in a notable reduction in computational complexity. Simulation results demonstrate the substantial potential of the proposed method in enhancing the localization performance for mixed-field sources.