Coordinate transformation and three-dimensional backprojection algorithm for multiple receiver synthetic aperture sonar motion compensation

Motion compensation (MoCo) is an important step for obtaining a high-quality image of synthetic aperture sonar (SAS). In this paper, a novel three-dimensional (3D) backprojection (BP) algorithm is proposed to solve the MoCo question for the multiple receiver SAS with the six degrees of freedom (DOF) motion error. In order to improve the MoCo capacity of the proposed 3D BP algorithm, some more accurate position data of sonar array are calculated by the method of space rectangular coordinate transformation. According to the inherent relationship between sonar array and inertial navigation system (INS), the position data of sonar array at the sampling time of INS data are obtained based on the position data and attitude data output by INS, without any approximation. On the basis, the relatively accurate position data of sonar array at the time of pulse transmission are obtained by the method of linear interpolation. Considering the movement of SAS during the period of signal propagation, the signal propagation time for each pulse and each receiver are calculated. Moreover, the position data of each receiver of SAS at the time of signal reception are obtained. Based on above derived position data, a well-focused SAS image is obtained and the six DOF motion error are compensated simultaneously by the 3D BP algorithm. The result of experiment demonstrates the validity of the proposed algorithm.