LM算法在稀疏矩阵光束法区域网平差中的应用
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摘要
通过介绍光束法区域网平差的误差方程和法方程的建立,针对解算法方程的算法进行了对比分析。针对高斯牛顿法在解算非线性模型最小化中存在的问题,提出将LM算法应用于非线性模型的最小化解算,并通过算例验证了LM算法的优越性。为了提高区域网平差的效率和实用性,相对于传统LM算法解算的稠密性,提出了在LM算法中采用稀疏矩阵的方法来解算光束法区域网平差的法方程,验证了将LM算法应用于稀疏矩阵光束法区域网平差的可行性。
In this paper, we established the error equation of the bundle-adjustment regional network method and normal equation, compared and analyzed the algorithm of the solution algorithm. We applied LM algorithm to the minimum solution of nonlinear model, and verified the advantages of the LM algorithm by an example. At the same time, in order to improve the efficiency and practicability of the regional network adjustment, we used the sparse matrix method in the LM algorithm to solve the normal equation of the bundle adjustment regional network method, according to the density of the traditional LM algorithm, which could prove the feasibility of LM algorithm in the bundle adjustment regional network method for sparse matrix.
In this paper, we established the error equation of the bundle-adjustment regional network method and normal equation, compared and analyzed the algorithm of the solution algorithm. We applied LM algorithm to the minimum solution of nonlinear model, and verified the advantages of the LM algorithm by an example. At the same time, in order to improve the efficiency and practicability of the regional network adjustment, we used the sparse matrix method in the LM algorithm to solve the normal equation of the bundle adjustment regional network method, according to the density of the traditional LM algorithm, which could prove the feasibility of LM algorithm in the bundle adjustment regional network method for sparse matrix.
引文
[1]詹总谦,张祖勋,张剑清.基于稀疏矩阵技术的光束法平差快速算法设计[J].测绘通报2006(12):5-8
[2]王新洲.非线性模型参数估计理论与应用[M].武汉:武汉大学出版社,2002
[3]陈朋山,焦伟利,等.抗差LM算法求解遥感影像严格物理模型[J].地球科学,2009,9(16):1 671-1 819
[4]胡志刚,花向红.Levenberg-Marquardt算法及其在测量模型参数估计中的应用[J].测绘工程,2008,17(4):31-34
[5]Manmohan,Krishna,Chandraker.Bundle Adjustment Sparse Estimation in Multi-View Geometry[J].CSE 252C,Fall 2004,UCSD
[6]Manolis A.Lourakis,Antionis A.Argyros.SBA:A Software Package for Generic Sparse Bundle Adjustment ACM Transactions on Mathematical Software[M].Vol.36,No.1,Article 2,March 2009
[7]Manolis I.A.Lourakis.A Brief Description of the LevenbergMarquardt Algorithm Implemened by Levmar[J].Institute of Computer Science,2005(3):1-6
[8]王佩军,许亚明.摄影测量学[M].武汉:武汉大学出版社,2005
[2]王新洲.非线性模型参数估计理论与应用[M].武汉:武汉大学出版社,2002
[3]陈朋山,焦伟利,等.抗差LM算法求解遥感影像严格物理模型[J].地球科学,2009,9(16):1 671-1 819
[4]胡志刚,花向红.Levenberg-Marquardt算法及其在测量模型参数估计中的应用[J].测绘工程,2008,17(4):31-34
[5]Manmohan,Krishna,Chandraker.Bundle Adjustment Sparse Estimation in Multi-View Geometry[J].CSE 252C,Fall 2004,UCSD
[6]Manolis A.Lourakis,Antionis A.Argyros.SBA:A Software Package for Generic Sparse Bundle Adjustment ACM Transactions on Mathematical Software[M].Vol.36,No.1,Article 2,March 2009
[7]Manolis I.A.Lourakis.A Brief Description of the LevenbergMarquardt Algorithm Implemened by Levmar[J].Institute of Computer Science,2005(3):1-6
[8]王佩军,许亚明.摄影测量学[M].武汉:武汉大学出版社,2005