联合一维到达角和到达时差的水下目标快速定位算法

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

针对水下洋流或工程测量等原因引起的传感器位置误差,以及仅使用单一观测参数造成的定位精度问题,本文提出一种联合一维到达角(One-Dimensional Angle of Arrival,1-D AOA)和到达时差(Time Difference of Arrival,TDOA)的水下目标快速定位算法,该算法通过锥面和双曲面的交点确定目标位置。首先,在观测噪声和线阵中点位置扰动噪声下,推导联合1-D AOA和TDOA观测值与目标位置的非线性方程。接着,提出一种两步加权最小二乘(Weighted Least Squares,WLS)求解算法,该算法第一步引入辅助变量将非线性方程转化为伪线性方程,并使用WLS获得目标位置的粗估计;第二步利用目标位置和辅助变量的关系构造新的方程,再用WLS得到更精确的目标位置估计。然后,推导了在观测噪声和线阵中点位置扰动噪声下的克拉美罗下界(Cramer-Rao lower bound,CRLB)来评估定位性能。仿真实验结果表明,与现有联合1-D AOA和TDOA测量的算法相比,所提算法考虑线阵中点位置误差,在传感器位置误差场景下具有更高的定位精度。

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 tar-get 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 influ-ence 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 measure-ments,the proposed algorithm considers linear array midpoint position errors and achieves higher positioning accuracy in scenarios with sensor location errors.