Broad-Learning-Based Localization for Underwater Sensor Networks With Stratification Compensation

Abstract

Localization is an indispensable service for underwater sensor networks (USNs). Generally, the convex optimization method is adopted to solve the localization problem. However, the acoustic ray in water medium does not propagate along a straight line, which makes it difficult or impossible to transform the non-convex optimization problem into a convex optimization problem. This paper develops a broad learning (BL) based localization solution for USNs with isogradient sound speed profile. We first employ the ray tracing model to compensate the range bias caused by straight-line propagation. On the basis of collected range information from anchor nodes, the localization optimization problem is transformed into supervised, unsupervised and semisupervised learning frameworks. Correspondingly, three BL-based location estimators are developed to seek the position information of sensor nodes, where the incremental learning schemes are conducted for fast parameter tuning and remodeling. In addition, the Cramer-Rao Lower Bound (CRLB) of positioning error and the convergence to global optimality are both analysed. Finally, simulation and experiment results are presented to show the effectiveness of our approach. It is demonstrated that the proposed solution in this paper has the following nice features: 1) relax the dependence of convex relaxation over convex optimization-based location estimators; 2) reduce the training time and improve the localization efficiency over deep learning-based location estimators.