基于迭代最小二乘的水下三维高鲁棒性定位算法

A Highly Robust Underwater 3D Localization Algorithm Based on Iterative Least Square

为解决基于空间角信息水下3维定位中,闭式解算法中定位性能无法达到克拉默-拉奥界(CRLB)和牛顿迭代算法初始值选取问题,该文利用一种基于迭代最小二乘的高鲁棒性算法修正闭式解的残差项与选取迭代算法的初始值。利用伪线性加权最小二乘算法得到闭式解作为正则化修正迭代法的初始值,将迭代结果修正闭式解算法的残差项,通过迭代最小二乘法的交替运算,得到稳定精确的解。通过仿真验证了基于迭代最小二乘算法的高鲁棒性,消除伪线性加权最小二乘算法中残差项选取的不利影响,解决了迭代法初始值选取问题,得到与收敛情况下迭代法相近的定位性能。

In order to solve the problem that the positioning performance of the closed solution algorithm can not reach the Cramer Rao Lower Bound(CRLB)and the initial value selection of Newton iterative algorithm in the underwater three-dimensional positioning based on spatial angle information,a highly robust algorithm based on iterative least squares is used to correct the residual term of the closed form solution and select the initial value of the iterative algorithm.The pseudo linear Weighted Least Squares(WLS)algorithm is used to obtain the closed form solution as the initial value of the regularization modified iterative method.The iterative result is used to modify the residual term of the closed form solution algorithm.Through the alternating operation of the iterative least squares method,a stable and accurate solution is obtained.Through simulation,the high robustness of the iterative least squares algorithm is verified,the adverse effect of the selection of the residual term in the pseudo linear weighted least squares algorithm is eliminated,the problem of selecting the initial value of the iterative method is solved,and the positioning performance similar to that of the iterative method in the case of convergence is obtained.