In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
基于点云的空间非合作目标位姿估计,常受到噪声影响.提出截断最小二乘估计与半定松弛(truncated least squares estimation and semidefinite relaxation,TEASER)与迭代最近点(iterative closest point,ICP)的结合算法,提升空间非合作...基于点云的空间非合作目标位姿估计,常受到噪声影响.提出截断最小二乘估计与半定松弛(truncated least squares estimation and semidefinite relaxation,TEASER)与迭代最近点(iterative closest point,ICP)的结合算法,提升空间非合作目标位姿估计精度与鲁棒性.该方法包括粗配准与精配准两个环节:在粗配准环节中,基于局部点云与模型点云的方向直方图特征(signature of histogram of orientation,SHOT)确定匹配对,利用TEASER算法求解初始位姿;在精配准环节中,可结合ICP算法优化位姿估计结果.北斗卫星仿真实验表明:在连续帧位姿估计中,噪声标准差为3倍点云分辨率时,基于TEASER的周期关键帧配准方法的平移误差小于3.33 cm,旋转误差小于2.18°;与传统ICP方法相比,平均平移误差与平均旋转误差均有所降低.这表明所提出的空间非合作目标位姿估计方法具有良好的精度和鲁棒性.展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
文摘基于点云的空间非合作目标位姿估计,常受到噪声影响.提出截断最小二乘估计与半定松弛(truncated least squares estimation and semidefinite relaxation,TEASER)与迭代最近点(iterative closest point,ICP)的结合算法,提升空间非合作目标位姿估计精度与鲁棒性.该方法包括粗配准与精配准两个环节:在粗配准环节中,基于局部点云与模型点云的方向直方图特征(signature of histogram of orientation,SHOT)确定匹配对,利用TEASER算法求解初始位姿;在精配准环节中,可结合ICP算法优化位姿估计结果.北斗卫星仿真实验表明:在连续帧位姿估计中,噪声标准差为3倍点云分辨率时,基于TEASER的周期关键帧配准方法的平移误差小于3.33 cm,旋转误差小于2.18°;与传统ICP方法相比,平均平移误差与平均旋转误差均有所降低.这表明所提出的空间非合作目标位姿估计方法具有良好的精度和鲁棒性.
