A sparse signal reconstruction perspective for hydrophone array shape calibration

The performance of array processing algorithms critically depends on the precise knowledge of the array shape. Calibration of array shape error must be obtained in advance. A high precision array shape calibration method using sources in known directions which can be applied to arbitrary array geometries is proposed. With the prior knowledge of the bound of senor location uncertainty, the problem of array shape estimation is transformed into the process of sparse signal reconstruction from multiple time measurements with overcomplete basis. A geometry error model combined with compressed sensing method is established. The convex objective function penalized by l₁-norm aimed to enforce sparsity is efficiently solved in second-order cone(SOC) programming framework. The l₁ SVD algorithm is used to summarize multiple time samples. The physical interpretation and algorithm implementation steps are also explained. Computer simulations indicate the effectiveness of the proposed method by comparing the estimator RMSE to the Cramer-Rao lower bound(CRLB). Other advantages include high calibration precision, robustness to direction of calibration sources and not requiring accurate initialization.