Maximum likelihood array calibration using particle swarm optimisation

Calibration of array shape error is a key issue for most existing source localisation algorithms. In this study, the far-field self-calibration and near-field pilot-calibration are carried out using unconditional maximum likelihood (UML) estimator whose objective function is optimised by particle swarm optimisation (PSO). A new technique, decaying diagonal loading (DDL), is proposed to enhance the performance of PSO at high signal-to-noise ratio (SNR) by dynamically lowering it, based on the counter-intuitive observation that the global optimum of the UML objective function is more prominent at lower SNR. Numerical simulations demonstrate that the UML estimator optimised by PSO with DDL is robust to large shape errors, optimally accurate and free of the initialisation problem. In addition, the DDL technique can be coupled with different global optimisation algorithms for performance enhancement. Mathematical analysis indicates that the DDL is applicable to any array processing problem where the UML estimator is employed.