Direct position determination algorithm for non-circular sources in the presence of mutual coupling and its theoretical performance analysis

This article proposes a direct position determination (DPD) algorithm for non-circular sources observed by a moving array using the self-calibration technique in the presence of mutual coupling. The method first utilises the symmetric Toeplitz property of uniform linear array matrices with mutual coupling and cyclic Toeplitz property of uniform circular array coupling matrix, realising the decoupled estimations of target position parameters and sensor error parameters. Then the position parameters of multiple non-circular are directly determined based on the subspace data fusion criterion in a decoupled manner, where the subspaces are obtained using the extended array data model with the non-circular properties of the sources. This results in a significant improvement in the accuracy of the target position estimation and the number of distinguishable sources compared to the traditional mutual coupling calibration algorithm. In addition, the theoretical mean square error expression for the position estimations of the proposed algorithm under the influence of finite sampling is derived based on the matrix perturbation analysis theory, and the corresponding Cramér-Rao bound is given. Finally, the correctness of the theoretical derivation and the superiority of the method is verified by simulation experiments.