Passive localization of mixed near-field and far-field sources using two-stage MUSIC algorithm

Passive source localization is one of the issues in array signal processing fields. In some practical applications, the signals received by an array are the mixture of near-field and far-field sources, such as speaker localization using microphone arrays and guidance (homing) systems. To localize mixed near-field and far-field sources, this paper develops a two-stage MUSIC algorithm using cumulant. The key points of this paper are: i) in the first stage, this paper derives one special cumulant matrix, in which the virtual "steering vector" is the function of the common electric angle in both near-field and far-field signal models so that source direction-of-arrival (DOA) (near-field or far-field one) can be obtained from this electric angle using the conventional high-resolution MUSIC algorithm; ii) in the second stage, this paper derives another particular cumulant matrix, in which the virtual "steering matrix" has full column rank no matter whether the received signals are multiple near-field sources or multiple far-field ones or their mixture. What is more important, the virtual "steering vector" can be separated into two parts, in which the first one is the function of the common electric angle in both signal models, whereas the second part is the function of the electric angle that exists only in near-field signal model. Furthermore, by substituting the common electric angle estimated in the first stage into one special Hermitian matrix formed from another MUSIC spectral function, the range of near-field sources can be obtained from the eigenvector of the Hermitian matrix. The resultant algorithm avoids two- dimensional search and pairing parameters; in addition, it avoids the estimation failure problem and alleviates aperture loss. Simulation results are presented to validate the performance of the proposed method.