A Fast Localization Algorithm for Underwater Targets Using Joint One-Dimensional Angle of Arrival and Time Difference of Arrival

‍ ‍To address the issues of low positioning accuracy due to underwater current drift or engineering measurement-induced sensor location errors and the use of only a single observation parameter， this paper proposes a fast underwater target positioning algorithm that jointly utilizes one-dimensional angle of arrival （1-D AOA） and time difference of arrival （TDOA）， which determines the target position by the intersection point of a cone and a hyperboloid. First， under the influence of observation noise and linear array midpoint position perturbation noise， we derived the nonlinear equation relating the joint 1-D AOA and TDOA observations to the target position. Next， we proposed a two-step weighted least squares （WLS） solving algorithm. In the first step， the algorithm introduces auxiliary variables to transform the nonlinear equation into a pseudo-linear equation and uses the WLS method to obtain a rough estimate of the target position. In the second step， the relationship between the target position and auxiliary variables is used to construct a new equation， and the WLS method is applied again to obtain a more accurate target position estimate. Subsequently， we derived the Cramer-Rao lower bound （CRLB） under observation noise and linear array midpoint position perturbation noise to evaluate positioning performance. Simulation results show that， compared to existing algorithms that jointly use 1-D AOA and TDOA measurements， the proposed algorithm considers linear array midpoint position errors and achieves higher positioning accuracy in scenarios with sensor location errors.