Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
滤波是机载激光扫描的核心处理步骤之一,其主要任务是分离地面点和非地面点。经典渐进式不规则三角网致密化(Progressive TIN Densification)在众多滤波算法中效果较好、精度较高,但是PTD滤波算法阈值确定需要人工干预,无法满足自适应...滤波是机载激光扫描的核心处理步骤之一,其主要任务是分离地面点和非地面点。经典渐进式不规则三角网致密化(Progressive TIN Densification)在众多滤波算法中效果较好、精度较高,但是PTD滤波算法阈值确定需要人工干预,无法满足自适应滤波。本文针对关键格网参数阈值提出等值线确定方法,利用等值线的连续性、闭合性,根据建筑物同一边缘区域的明显高差来确定最大建筑面积与格网的参数阈值。实验证明通过等值线确定的面积与格网参数阈值对于具有建筑物的复杂地形有着更好的滤波效果。展开更多
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
文摘滤波是机载激光扫描的核心处理步骤之一,其主要任务是分离地面点和非地面点。经典渐进式不规则三角网致密化(Progressive TIN Densification)在众多滤波算法中效果较好、精度较高,但是PTD滤波算法阈值确定需要人工干预,无法满足自适应滤波。本文针对关键格网参数阈值提出等值线确定方法,利用等值线的连续性、闭合性,根据建筑物同一边缘区域的明显高差来确定最大建筑面积与格网的参数阈值。实验证明通过等值线确定的面积与格网参数阈值对于具有建筑物的复杂地形有着更好的滤波效果。
