Research on TMR-FCN-based underwater projectile localization method

Abstract

A machine learning localization method for underwater projectile using Tunnel magnetoresistance (TMR) sensors is proposed in this paper. Firstly, the relation between the magnetic field intensity and the position of the projectile was built based on the magnetic dipole model. Then, the measurement model of TMR sensors was constructed to offer the voltage signal linearly correlated to the magnetic field intensity, and the network model based on the fully connected neural network (FCN) was established to approximate and regress the highly nonlinear mapping function between the magnetic field intensity (B) and the square of the distance from the projectile to the sensor (d2). Inspired by the Received Signal Strength (RSS) localization method, the least-square method was adopted to solve the actual coordinate of the projectile. Finally, to verify the localization accuracy of the proposed TMR-FCN-based method, the ballistic simulation was performed for providing the actual position of the projectile and the output of the TMR sensors, then the positioning operation was carried out by coupling the FCN model and the least-square method. The results demonstrate that the B-d2 model can fast compute the d2 within 8ms for the single given B and the overall mean accuracy is up to 99.15%. The localization distance error via the least-square method is lower than 0.5mm. These results indicate that the TMR-FCN-based localization method can achieve accurate localization for the underwater projectile and effectively overcome the tough problem of solving the high-dimensional nonlinear equations for B and d2.