Underwater LBL Positioning Based on Gauss Kernel B-Spline for Fitting the SSP in IoUT Networks

The high-accuracy positioning of autonomous underwater vehicles (AUVs) is important in the Internet of Underwater Things (IoUT). AUV positioning relies on acoustic signal measurement systems. Owing to the variation in sound speed, the acoustic signal path is curved. The straight-line distance from an AUV to a measurement system cannot be simply calculated using the product of the propagation time and sound speed. Therefore, a time of arrival (TOA) positioning model is proposed to avoid calculating the straight-line distance, which is based on the continuous sound speed profile (SSP) ray tracing method. This model does not require knowing the depth of the AUV in advance. In addition, an improved Gauss-Newton iteration method based on the effective sound speed (ESS) is proposed to estimate the AUV position. The distance residual in the improved iteration is calculated on the basis of the time residual and the ESS, which is more accurate. Because the measured SSP is discrete data and cannot be directly used for the TOA positioning model, a Gauss kernel B-spline is proposed to obtain the continuous SSP. By optimizing the parameter $\sigma $ , a high-accuracy continuous SSP can be obtained. Furthermore, theoretical analyses, including the Cramér-Rao lower bound (CRLB) and complexity of the algorithm are also provided. The simulation results show that, compared with the 10th-degree polynomial and cubic standard B-spline, the Gauss kernel B-spline effectively improves the fitting accuracy. Compared with the traditional sound speed model and the current isogradient ray tracking model, the proposed TOA positioning model has better AUV positioning accuracy and is closer to CRLB.