全局收敛L-M迭代法的非线性参数平差  

Globally convergent levenberg-marquardt method for nonlinear parameter adjustment

作　　者：王利朋[1,2] 刘成龙[1,2] 

机构地区：[1]西南交通大学地球科学与环境工程学院,四川成都611756 [2]西南交通大学高速铁路运营安全空间信息技术国家地方联合工程实验室,四川成都611756

出　　处：《铁道科学与工程学报》2015年第6期1452-1457,共6页Journal of Railway Science and Engineering

基　　金：长江学者和创新团队发展计划资助项目(IRT13092)

摘　　要：采用全局收敛的L-M非线性迭代算法,可以较大程度减弱非线性模型线性化的模型误差,在雅可比矩阵近似奇异或坏条件时,L-M迭代仍然可以收敛;同时,该算法具有全局收敛特性,大大降低了平差对迭代初值的要求,可以在初值受误差影响较大的情况下得到精确解。通过与几种不同的非线性规划算法的比较,证明了全局收敛的L-M迭代算法无论是解算精度还是收敛范围均具有相对优势。Adopting iterated algorithm of globally convergent levenberg- marquardt could weaken the model error greatly while non- linear model is linearized. Beside,the L- M iterated algorithm is still convergent even Jacobian matrix is approximatively singular. Meanwhile,the algorithm is globally convergent which would weaken the requirement greatly for iterative initial value. This algorithm could gain exact solution even the iterative initial value has a serious error. Through the comparison of different non- linear programming algorithm,it has been proved that iterated algorithm of globally convergent levenberg- marquardt has comparative advanage in accuracy and the range of convergence.

关 键 词：全局收敛 L-M迭代 非线性参数平差 模型误差 

分 类 号：P207[天文地球—测绘科学与技术]