Fig. 3

Synthetic test results assuming the square-formed array geometry. Kinematic array positioning results of the synthetic data assuming the square-formed array geometry (Fig. 2a) are shown: a east–west component of array positions, b north–south component of array positions, c vertical component of array positions, d NTD, e east–west component of underwater delay gradient, and f north–west component of underwater delay gradient. Cyan curves represent the true values for the synthetic data. Black triangles, orange crosses, blue squares, and purple circles show the results estimated by conventional array positioning fixing the vertical component, conventional array positioning solving the vertical component, EKF-based array positioning assuming a laterally stratified sound speed structure, and EKF-based array positioning assuming a horizontally graded sound speed structure, respectively