Localisation and classification of mixed far-field and near-field sources with sparse reconstruction

A sparse reconstruction algorithm for the localisation of mixed near-field and far-field sources (MFNS) based on four-order statistics is proposed in this study. First, utilising the structural characteristics of a uniform symmetric linear array, a fourth-order cumulant (FOC) matrix is constructed, which decouples the angular information from the range parameters. Based on the sparse representation framework, a weighted l₁-norm minimisation algorithm is developed to obtain the direction of arrivals (DOAs) of the MFNS. However, the existing selection strategy of the tuning factor is not adaptive to different observation scenarios. So a closed-form expression of the tuning factor based on the FOC estimation error is presented. Then, another FOC matrix is constructed, which includes both the DOA and range information of the MFNS. With the DOA estimates, the two-dimensional spatial dictionary can be reduced into a one-dimensional dictionary, which only depends on the range parameters. Using the similar sparse reconstruction method, the range estimates of the MFNS can be obtained, and the types of the sources can be distinguished according to their range parameters. According to numerical simulations, the estimation performance of the proposed algorithm approaches the CRB in the high signal-to-noise ratio region, which successfully circumvents the saturation problem due to the fixed tuning factor.