1.湖南大学 数学学院;2.国防科技大学气象海洋学院;3.湖南大学数学学院
国家自然科学基金项目（面上项目，重点项目，重大项目）
1.School of Mathematics,Hunan University;2.College of Meteorology and Oceanography，National University of Defense Technology
利用三轴磁传感器阵列对水下磁性目标进行定位是典型的非线性最小二乘优化问题,传统高斯牛顿法(GN)和列文伯格-马夸尔特(LM)算法在求解该问题时具有初值敏感性问题,本文通过引入信赖域搜索技术,对LM算法进行改进,并基于改进的LM算法实现磁性目标定位,又通过设置判断阈值来评估迭代点与最优解的距离,提出一种结合改进LM算法和高斯牛顿法特点的改进LM-GN算法,既降低了算法对初始值的依赖性,又提高了运行效率。仿真实验结果表明,该方法可以克服现有方法中受初始值影响较大的问题,对目标特征参数的估计更精确,且收敛速度快,具有一定的实际应用价值。
The use of three-axis magnetic sensor array to locate underwater ferromagnetic target is a typical nonlinear least squares optimization problem. Traditional Gaussian-Newton method (GN) and Levenberg-Marquardt (LM) algorithm have an initial sensitivity problem when solving this problem. This paper improves the LM algorithm by introducing the trust domain search technology, and realizes magnetic target localization based on the improved LM algorithm, then the distance between the iteration point and the optimal solution is evaluated by setting the threshold value, and proposes an improved LM-GN algorithm combining the characteristics of the improved LM algorithm and Gaussian-Newton method. It not only reduces the dependence of the algorithm on the initial value, but also improves the operation efficiency. The simulation results show that the proposed method can overcome the problem of the existing methods which are greatly affected by the initial value, and the estimation of the target characteristic parameters is more accurate and the convergence rate is fast, so it has certain practical application value.
