摘要
Levenberg-Marquardt(LM)算法是一种求解非线性模型的数值算法,已成功地应用于最小二乘曲线拟合和非线性最优化中。LM算法能克服Hessian矩阵病态对解的影响,但是不能抵抗输入样本中粗差的干扰。为消除粗差对求解模型的影响,将等价权思想应用于LM算法中,对LM算法中的样本添加权重,得到抗差LM算法。通过其在Landsat5和SPOT5几何校正模型中应用,验证了该算法具有良好的抗差性,可以解决遥感图像校正模型解算过程中粗差的影响问题。
Levenberg-Marquardt （LM） algorithm provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function. It now has been widely used in many fields for solving generic curve-fitting problems. LM can be thought of as a combination of steepest descent and the Gauss-Newton method. Compared with Gauss-Newton method, it is more robust because it can overcome the obstacle of ill-conditioned normal equations. Nevertheless, the solution will deviate from its mathematical expectation, when the outliers exist in the samples. In order to eliminate the influence of the gross errors, referring the equivalent weights method, this paper proposes the robust LM algorithm. The algorithm has been carried out in the Regious Physical Models of SPOT5 and Landsat5 images. It shows that the robust LM estimator can efficiently dismiss the influence of the outlier and can get the robust parameters of the rectification model.
出处
《科学技术与工程》
2009年第16期4614-4618,共5页
Science Technology and Engineering
基金
国家高技术研究发展计划(863计划)(2006AA12Z118)资助
关键词
严格物理模型LM算法
抗差
权函数
粗差
regious physical model LM algorithm robust weight function gross error
