Turning towed array shape self-calibration via multistage constant modulus array

When the tow vessel was turned, beamforming and the directions-of-arrival (DOA) estimation would be critically degraded if the horizontal towed linear array shape was still assumed to be a straight line. An effective method was proposed to self-calibrate the bended towed array shape based on the blind signal separation, which could simultaneously estimate the DOA and the sensor locations. Firstly, the arbitrary number of incident independent signals and their corresponding steering vectors were blindly recovered from the output of the multistage constant modulus (CM) array without any information of the towed array shape. Then, based on the estimated steering vectors, the array shape self-calibration problem could be described as a nonlinear constrained least-squares problem and solved by the genetic algorithm. Finally, the Cramér-Rao bounds (CRB) for the estimation was derived and computer simulations were conducted. It was shown that the signal reconstruction ability was not affected by the towed array shape deformation magnitude and the interference could be adaptively restrained by using the multistage CM array. Results from the simulations verified that the proposed method can not only blindly recover the incident signals, but also effectively estimate the DOA and the bended towed array shape.