Joint calibration of array shape and sensor gain/phase for highly deformed arrays using wideband signals

A joint sensor position and gain/phase calibration method for highly deformed arrays is proposed. It applies to the case where the sensor gain is omnidirectional and frequency-invariant, and the sensor phase is directional and frequency-invariant. The method is initialized with the raw estimates of the sensor gains, which are simply obtained from the main diagonal elements of the sample covariance matrix. Then, it alternately updates either the sensor gain estimates or the sensor position and phase estimates while fixing the other. When the sensor gain estimates are available, the steering matrices for all the frequency bins are estimated using the constant modulus method. By combining all these steering matrices, the estimates of the sensor positions and the frequency-invariant sensor phases are straightforwardly derived. Then, the sensor gain estimates are refined for the next iteration by using the orthogonality of the subspaces. To resolve the phase ambiguities due to the large position mismatches of highly deformed arrays, the nominal intersensor distance and the array bending angle are used. The Cramer–Rao lower bounds (CRLBs) for the unknown sensor gain/phase and position are also derived. The performance of the proposed method is evaluated using simulation data and compared with the CRLBs.