Research On Positioning Technology Of Underwater Sensor Networks Based On Convex Optimization Algorithm

In recent years,underwater sensor networks have played an increasingly important role in environmental monitoring,target detection and underwater vehicle positioning and navigation,attracting many scholars to research in the application of underwater sensor networks.In underwater sensor networks,obtaining high-precision position of underwater nodes is the basis of underwater sensor networks applications.The high-precision position of underwater nodes is a powerful guarantee for the validity of underwater data acquisition and the reliability of target location.However,the underwater environment is complex and highly dynamic,which makes the positioning of underwater sensor networks a great challenge.In this paper,the position error of anchor nodes and unknown propagation speed in underwater sensor networks are analyzed,and a high-precision robust location algorithm is studied.At present,in underwater sensor network positioning,the time measurement errors between nodes are usually considered,while the position errors of anchor nodes are neglected.In fact,the location errors of anchor nodes have become one of the main problems restricting high-precision positioning due to the factors such as the layout of nodes and the flow of water.Based on the assumption that the location errors of anchor nodes and the time-measuring errors between nodes obey Gauss distribution,this paper constructs a location model of network nodes based on maximum likelihood estimation criterion,and introduces second-order cone programming(SOCP),semi-definite programming(SDP)and DC programming algorithm to solve the optimal solution of the location model.The effectiveness of the three convex optimization algorithms is verified by simulation,at the same time,the advantages and disadvantages of the three convex optimization algorithms are also compared and analyzed.In addition,due to the distinct vertical stratification of sound velocity distribution in seawater,the phenomenon of sound line bending is obvious,and the apparent distance can only be obtained after correction.In order to restrain the influence of sound velocity error on node positioning accuracy,this paper uses Snell's law to eliminate the location error caused by unknown sound velocity when solving the optimization model combined with underwater sound velocity profile information.The simulation verifies that the sound ray tracking algorithm can effectively eliminate the positioning error caused by sound velocity.Then,considering that it is difficult for all nodes in underwater sensor networks for long-term ocean monitoring to acquire real-time data and the computational complexity of the sound ray tracking algorithm is high,this paper,under the assumption that the equivalent average sound velocity between nodes is equal in one positioning process,generates it as an unknown quantity into the basic positioning model to solve the problem.Based on semi-definite programming(SDP),the different positioning model for solving sound velocity in the condition of considering or not considering the position error of anchor nodes are proposed.In the condition of considering the position error of anchor nodes,the SDP positioning model for solving sound velocity can not converge to the optimal solution.At this time,DC programming is used to improve the positioning result and the estimation value of sound velocity,which can converge to the optimal solution.And the validity of the positioning model for solving the sound velocity is verified by simulation.Finally,by processing and analyzing the data of lake and sea trials respectively,it is proved that the convex optimization positioning algorithms presented in this paper have higher positioning accuracy and robustness than the conventional least squares algorithm.In the process of lake trial data,because the calibration error of anchor node is in centimeter level and the lake environment changes slightly,the average positioning accuracy of the convex optimization algorithm presented in this paper is basically consistent with that of the conventional least squares algorithm.While in the sea trial environment,the calibration error of anchor node is in meter level and the sea environment changes greatly,the average positioning accuracy of the proposed convex optimization positioning algorithm is maximumly improved by nearly 1m.Under the condition of unknown underwater sound velocity,the convex optimization positioning algorithm for solving sound velocity can achieve the same or even better positioning performance than the conventional least squares algorithm which knows the reference equivalent average sound velocity.