CAJ | 학술논문

针对大规模、近病态法的近景区域网平差法方程快速解算问题,提出基于预处理共轭梯度( preconditioned conjugate gradient,PCG)法的稀疏解算方法。首先,通过选择与法方程系数矩阵对应的对角平方根矩阵作为预处理矩阵,以改变待估参数向量的坐标基,进而改善法方程系数矩阵性态,达到利用PCG提高收敛速度和解算精度的目的；然后,通过应用稀疏矩阵提高平差法方程系数矩阵的储存与求解效率。实验结果证明,该方法不影响摄影测量中区域网平差中多类、多尺度参数同时解算的收敛域,不但具有很高的解算精度,而且速度较快。
침대대규모、근병태법적근경구역망평차법방정쾌속해산문제,제출기우예처리공액제도( preconditioned conjugate gradient,PCG)법적희소해산방법。수선,통과선택여법방정계수구진대응적대각평방근구진작위예처리구진,이개변대고삼수향량적좌표기,진이개선법방정계수구진성태,체도이용PCG제고수렴속도화해산정도적목적；연후,통과응용희소구진제고평차법방정계수구진적저존여구해효솔。실험결과증명,해방법불영향섭영측량중구역망평차중다류、다척도삼수동시해산적수렴역,불단구유흔고적해산정도,이차속도교쾌。
Aimed at tackling the fast solver problem for the large-scale and nearly pathological close-range block sparse bundle adjustment normal equation, the authors propose a solution method based on the preconditioned conjugate gradient( PCG) sparse algorithm. Firstly,the normal equation coefficient matrix corresponding to diagonal matrix square root is selected as the preconditioning matrix by changing the coordinate base of the parameter vector to be estimated, which can improve the behavior of the normal equation coefficient matrix so as to achieve the purpose of improving the convergence rate of the conjugate gradient method. Then, through the application of the sparse matrix, the efficiency of storage can be improved and the adjustment of normal equation coefficient matrix can be achieved. Experiment results show that the method proposed in this paper has the advantage that any scalar change in variables has no effect on the range of convergence of the iterative technique,and hence it has not only high accuracy of calculation but also faster speed.