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A direct proof of uniqueness of square-root of a positive semi-definite tensor
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作者 邵玥 吕存景 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第6期713-716,共4页
Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square... Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor. 展开更多
关键词 positive semi-definite tensor second-order tensor UNIQUENESS decomposi-tion
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Positive definiteness of fourth-order partially symmetric tensors
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作者 WANG Hua-ge 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第4期581-590,共10页
In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dim... In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dimensional partially symmetric tensors.Then,we obtain several sufficient conditions for rank-one positive definiteness of fourth-order three dimensional partially symmetric tensors. 展开更多
关键词 partially symmetric tensor positive de niteness rank-one positive de nite
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ON SHRINKING GRADIENT RICCI SOLITONS WITH POSITIVE RICCI CURVATURE AND SMALL WEYL TENSOR 被引量:1
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作者 Zhuhong ZHANG Chih-Wei CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1235-1239,共5页
We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ... We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler. 展开更多
关键词 SHRINKING GRADIENT RICCI SOLITONS positive RICCI curvature pinched WEYL tensor
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<i>H</i>-Singular Value of a Positive Tensor
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作者 Jun He 《Advances in Linear Algebra & Matrix Theory》 2015年第1期16-24,共9页
In this paper we study properties of H-singular values of a positive tensor and present an iterative algorithm for computing the largest H-singular value of the positive tensor. We prove that this method?converges for... In this paper we study properties of H-singular values of a positive tensor and present an iterative algorithm for computing the largest H-singular value of the positive tensor. We prove that this method?converges for any positive tensors. 展开更多
关键词 SINGULAR VALUE positive tensor CONVERGENCE
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The Path-Positive Property on the Products of Graphs
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作者 连广昌 《Journal of Southeast University(English Edition)》 EI CAS 1998年第2期130-134,共5页
The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ... The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively. 展开更多
关键词 product of graphs path positive property Cartesian product of graphs tensor product of graphs lexicographic product of graphs strong direct product of graphs
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Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement 被引量:5
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作者 WANG Sansheng ZHANG Mingji +1 位作者 ZHANG Ning GUO Qiang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第3期456-461,共6页
Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tens... Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object(2.44 Am^2@1 kHz) can be increased from(0.45 m, 0.75 m),(0?, 25?) to(0.30 m, 0.80 m),(0?,80?), respectively. 展开更多
关键词 magnetic dipole magnetic gradient tensor positioning error error correction
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基于伪磁梯度张量混合方向tilt梯度的磁源定位方法及其应用:以内蒙古塔木素铀矿床为例
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作者 王彦国 林昭翰 +3 位作者 邓居智 郭华 郝梦成 Sulaiman Garba Yana 《地球物理学报》 SCIE EI CAS CSCD 北大核心 2024年第5期2043-2056,共14页
斜磁化磁源的准确定位是磁法勘探有效圈定场源分布及划分断裂构造的重要依据.但受磁化方向影响,总磁异常与地质体分布并无明显对应关系.为此,本文从总磁异常垂向积分出发,推导出了伪磁梯度张量,定义了伪磁梯度张量的混合方向tilt梯度及... 斜磁化磁源的准确定位是磁法勘探有效圈定场源分布及划分断裂构造的重要依据.但受磁化方向影响,总磁异常与地质体分布并无明显对应关系.为此,本文从总磁异常垂向积分出发,推导出了伪磁梯度张量,定义了伪磁梯度张量的混合方向tilt梯度及混合方向解析信号振幅,提出了基于伪磁梯度张量混合方向tilt梯度水平导数组合的场源定位方法.模型试验表明,相对于解析信号振幅、tilt梯度的总水平导数及方向tilt梯度的总水平导数模这3种受磁化方向影响较小的方法,本文提出的磁源定位方法能够更有效地反映出不同磁化方向的磁源位置,具有更强的识别能力和定位精度.在内蒙古塔木素铀矿床的航磁资料应用中,新方法较好地展示出了已知断裂带的展布及出露岩浆岩的分布,同时有效地提取了塔木素铀矿床上方的弱磁异常信息,处理结果为研究区圈定隐伏岩体、划分隐伏断裂及扩大铀矿找矿靶区提供了依据. 展开更多
关键词 总磁异常 磁梯度张量 方向tilt梯度 磁源定位 塔木素铀矿床
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POSITIVE DEFINITE AND SEMI-DEFINITE SPLITTING METHODS FOR NON-HERMITIAN POSITIVE DEFINITE LINEAR SYSTEMS 被引量:1
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作者 Na Huang Changfeng Ma 《Journal of Computational Mathematics》 SCIE CSCD 2016年第3期300-316,共17页
In this paper, we further generalize the technique for constructing the normal (or pos- itive definite) and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system ... In this paper, we further generalize the technique for constructing the normal (or pos- itive definite) and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting (PPS) methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods. 展开更多
关键词 Linear systems Splitting method Non-Hermitian matrix positive definitematrix positive semi-definite matrix Convergence analysis.
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THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING
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作者 Si-ming Huang(Institute of Policy and Management, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China) 《Journal of Computational Mathematics》 SCIE CSCD 2003年第3期339-346,共8页
In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an alg... In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming. 展开更多
关键词 positive semi-definite programming Potential reduction algorithms Complexity.
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Generalized Inversions of Hadamard and Tensor Products for Matrices
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作者 Saburou Saitoh 《Advances in Linear Algebra & Matrix Theory》 2014年第2期87-95,共9页
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
关键词 Reproducing Kernel positive Definite HERMITIAN MATRIX tensor PRODUCT HADAMARD PRODUCT GENERALIZED Inverse MATRIX Equation Tikhonov Regularization 100/0 = 0 0/0 = 0 GENERALIZED Fraction GENERALIZED Fractional Function
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基于张量不变量及避免椭圆误差的定位方法研究 被引量:2
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作者 荆志伟 裴东兴 郭德月 《电光与控制》 CSCD 北大核心 2023年第3期54-57,69,共5页
针对目前广泛使用的基于磁梯度张量不变量的磁性目标定位方法未考虑椭圆系数的变化而导致定位精度降低这一问题,提出一种新的单位距离矢量求解方法和距离矢量模求解方法。通过分析磁性目标与测量系统之间的位置关系,构建新的单位距离矢... 针对目前广泛使用的基于磁梯度张量不变量的磁性目标定位方法未考虑椭圆系数的变化而导致定位精度降低这一问题,提出一种新的单位距离矢量求解方法和距离矢量模求解方法。通过分析磁性目标与测量系统之间的位置关系,构建新的单位距离矢量,并通过麦克劳林公式和磁梯度张量不变量分别构建新的存在一阶误差与二阶误差的距离矢量模,避免未考虑椭圆系数变化而导致定位精度降低。仿真试验验证了所提方法较以前方法定位精度有明显提升,存在一阶误差与二阶误差的距离矢量模对定位精度的影响基本相同。该方法对进行探潜和未爆炸物的检测等方面具有较高的研究和应用价值。 展开更多
关键词 磁性目标 目标定位 椭圆误差 麦克劳林公式 张量不变量 定位
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磁梯度张量不变量约束条件下的两点定位方法
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作者 迟铖 王丹 +3 位作者 于振涛 余路 秦锋 祝尚明 《水下无人系统学报》 2023年第4期582-587,共6页
文中针对单点磁梯度张量定位方法受地磁场估计误差影响较大,同时多点磁梯度张量定位方法容易陷入局部最优解等问题,提出一种两点磁梯度张量定位方法。该方法在单点磁梯度张量定位算法的基础上,采用两点磁梯度张量测量数据,叠加张量几何... 文中针对单点磁梯度张量定位方法受地磁场估计误差影响较大,同时多点磁梯度张量定位方法容易陷入局部最优解等问题,提出一种两点磁梯度张量定位方法。该方法在单点磁梯度张量定位算法的基础上,采用两点磁梯度张量测量数据,叠加张量几何不变量的约束条件,构建关于目标位置坐标的非线性目标函数,采用基于自然选择的粒子群算法对目标位置坐标进行求解。仿真实验表明,文中提出的方法受地磁场估计误差影响较小,且能实现对全局最优解的搜索,定位精度较高。仿真分析不同系统基线长度和磁力仪灵敏度条件下文中方法对磁性目标的定位效果可知,当系统的基线长度越大,磁力仪的灵敏度越高,磁性目标定位误差越小。 展开更多
关键词 磁梯度张量 几何不变量 两点定位 自然选择粒子群算法
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基于交变信号源的磁定位技术研究
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作者 郝伯强 郭锋 +1 位作者 赖禹同 唐自强 《传感器与微系统》 CSCD 北大核心 2023年第2期56-58,63,共4页
针对磁偶极子定位系统中静态磁信号源产生的静态磁场容易受到背景磁场和环境噪声的干扰的问题,提出了以交变磁场作为磁信号源进行梯度张量定位,研究了其稳定性。以正弦交变磁场信号为发射源,并利用锁相放大器实现对交流信号的解调,通过... 针对磁偶极子定位系统中静态磁信号源产生的静态磁场容易受到背景磁场和环境噪声的干扰的问题,提出了以交变磁场作为磁信号源进行梯度张量定位,研究了其稳定性。以正弦交变磁场信号为发射源,并利用锁相放大器实现对交流信号的解调,通过单点定位算法完成定位。实验结果表明:当噪声的信噪比逐渐减小时,静态磁源的绝对定位误差明显增大,而交变磁源定位系统受环境噪声的影响较小,具有较强的稳定性。 展开更多
关键词 磁定位 交变磁场 梯度张量 锁相放大
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LINEAR CONVERGENCE OF THE LZI ALGORITHM FOR WEAKLY POSITIVE TENSORS 被引量:3
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作者 Liping Zhang Liqun Qi Yi Xu 《Journal of Computational Mathematics》 SCIE CSCD 2012年第1期24-33,共10页
We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim... We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim(LZI) algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors. 展开更多
关键词 Irreducible nonnegative tensor Weakly positive tensor Largest eigenvalue Linear convergence.
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Linear operators and positive semidefiniteness of symmetric tensor spaces 被引量:4
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作者 LUO Zi Yan QI Li Qun YE Yin Yu 《Science China Mathematics》 SCIE CSCD 2015年第1期197-212,共16页
We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to sev... We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences.We prove a decomposition invariance theorem for linear operators over the symmetric tensor space,which leads to several other interesting properties in symmetric tensor spaces.We then consider the positive semidefiniteness of linear operators which deduces the convexity of the Frobenius norm function of a symmetric tensor.Furthermore,we characterize the symmetric positive semidefinite tensor(SDT)cone by employing the properties of linear operators,design some face structures of its dual cone,and analyze its relationship to many other tensor cones.In particular,we show that the cone is self-dual if and only if the polynomial is quadratic,give specific characterizations of tensors that are in the primal cone but not in the dual for higher order cases,and develop a complete relationship map among the tensor cones appeared in the literature. 展开更多
关键词 symmetric tensor symmetric positive semidefinite tensor cone linear operator SOS cone
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Hypergraph characterizations of copositive tensors 被引量:1
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作者 Yue WANG Jihong SHEN Changjiang BU 《Frontiers of Mathematics in China》 SCIE CSCD 2021年第3期815-824,共10页
A real symmetric tensor A=(ai_(1…im))∈R^([m,n]) is copositive(resp.,strictly copositive)if Ax^(m)≥0(resp.,Ax^(m)>0)for any nonzero nonnegative vector x∈ℝ^(n).By using the associated hypergraph of A,we give nece... A real symmetric tensor A=(ai_(1…im))∈R^([m,n]) is copositive(resp.,strictly copositive)if Ax^(m)≥0(resp.,Ax^(m)>0)for any nonzero nonnegative vector x∈ℝ^(n).By using the associated hypergraph of A,we give necessary and sufficient conditions for the copositivity of A.For a real symmetric tensor A satisfying the associated negative hypergraph H−(A)and associated positive hypergraph H+(A)are edge disjoint subhypergraphs of a supertree or cored hypergraph,we derive criteria for the copositivity of A.We also use copositive tensors to study the positivity of tensor systems. 展开更多
关键词 Copositive tensor HYPERGRAPH positive system
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Separability for Positive Operators on Tensor Product of Hilbert Spaces
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作者 Jin Chuan HOU Jin Fei CHAI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2021年第6期893-910,共18页
The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information theory.Mathematically,a quantum state is a trace-class positive operator with tr... The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information theory.Mathematically,a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert space.In this paper,in more general frame,the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert spaces.However,not like the quantum state case,there are different kinds of separability for positive operators with different operator topologies.Four types of such separability are discussed;several criteria such as the finite rank entanglement witness criterion,the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established;some methods to construct separable positive operators by operator matrices are provided.These may also make us to understand the separability and entanglement of quantum states better,and may be applied to find new separable quantum states. 展开更多
关键词 Hilbert spaces tensor products positive operators SEPARABILITY ENTANGLEMENT
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On the Bound of the Eigenvalue in Module for a Positive Tensor
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作者 Wen Li Wei-Hui Liu Seak-Weng Vong 《Journal of the Operations Research Society of China》 EI CSCD 2017年第1期123-129,共7页
In this paper,we propose a bound for ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor.From this bound,one may deduce the bound of the second largest eigenvalue in modul... In this paper,we propose a bound for ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor.From this bound,one may deduce the bound of the second largest eigenvalue in module for a positive tensor,and the bound can reduce to the matrix cases. 展开更多
关键词 positive tensors EIGENVALUE BOUND
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Completely positive tensors in the complex field
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作者 Anwa Zhou Jinyan Fan Qingwen Wang 《Science China Mathematics》 SCIE CSCD 2020年第6期1219-1234,共16页
In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the... In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained. 展开更多
关键词 complex completely positive tensor complex completely positive decomposition truncated moment problem semidefinite program
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基于差分的磁偶极子单点张量定位方法 被引量:14
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作者 李光 随阳轶 +1 位作者 刘丽敏 林君 《探测与控制学报》 CSCD 北大核心 2012年第5期50-54,共5页
采用单点测量的磁场矢量及磁张量数据进行磁偶极子定位的方法,受地磁场干扰大,极大地限制了其实用性。为此,提出基于差分的磁偶极子单点张量定位方法,设计出磁张量测量系统。该方法采用差分方式,消除地磁场及其他共模干扰。仿真结果表明... 采用单点测量的磁场矢量及磁张量数据进行磁偶极子定位的方法,受地磁场干扰大,极大地限制了其实用性。为此,提出基于差分的磁偶极子单点张量定位方法,设计出磁张量测量系统。该方法采用差分方式,消除地磁场及其他共模干扰。仿真结果表明:在地磁场存在的情况下原方法基本上无法实现定位,而该方法则具有较高的定位精度,当探测距离为17.320 5m时,定位误差仅有0.002 3m。 展开更多
关键词 磁张量 磁偶极子 定位 地磁场
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