Optimal Attitude Determination from Vector Sensors Using Fast Analytical Singular Value Decomposition

Liu, Zhuohua; Liu, Wei; Gong, Xiangyang; Wu, Jin

doi:10.1155/2018/6308530

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…For instance, Yang et al developed an analytical method for rootsolving of quartic equation [31]. And a novel analytical SVD method is proposed recently by us to conduct factorization of 3×3 matrix [32]. These methods are faster than representative numerical ones.…”

Section: Experiments and Comparisonsmentioning

confidence: 99%

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Fast Symbolic 3-D Registration Solution

Liu

Zhou

et al. 2020

IEEE Trans. Automat. Sci. Eng.

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3D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this paper by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost %50 to %80, on both personal computer and embedded processor.Note to Practitioners-3D registration usually has large computational burden in engineering tasks. The proposed symbolic solution can directly solve the eigenvalue and its associated eigenvector. A lot of computation resources can then be saved for better overall system performance. The deterministic behavior of the proposed solver also ensures long-endurance stability and can help engineer better design thread timing logic.

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Section: Experiments and Comparisonsmentioning

confidence: 99%

“…The N aN value stands for the 'Not a Number' one which is usually caused by indefinite devisions like 0 0 and ∞ ∞ . Here, the 'SVD' and 'EIG' are implemented using MATLAB internal functions while 'EIG Analytical' is from [31] and 'SVD Analytical' refers to [32].…”

Section: A Accuracy and Robustness Performancementioning

confidence: 99%

Fast Symbolic 3-D Registration Solution

Liu

Zhou

et al. 2020

IEEE Trans. Automat. Sci. Eng.

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show abstract

“…As far as the robustness is concerned, the SVD in fact has analytical version that is recently proposed by us [31]. However, such method has been proved to be unstable on robustness in real applications [29].…”

Section: With the Dragon Example Presented By Computer Graphicsmentioning

confidence: 99%

“…This indicatess even faster computation speed using compilingrun coding. Next, we rewrite the codes of SVD [11], fast analytical SVD [31], EIG [12], improved symbolic EIG [32] and our proposed FA3R for PC and embedded platforms using C++. We first generate a case where the SNR is 10 and it contains 10000 matched point correspondences.…”

Section: B Execution Time Complexitymentioning

confidence: 99%

“…3: The convergence performance of the proposed FA3R where the y-axis is the natural logarithm of the metric error. As far as the robustness is concerned, the SVD in fact has analytical version that is recently proposed by us [31]. However, such method has been proved to be unstable on robustness in real applications [29].…”

Section: A Accuracy Convergence and Robustnessmentioning

confidence: 99%

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Rigid 3D Registration: A Simple Method Free of SVD and Eigen-Decomposition

2020

IEEE Trans. Instrum. Meas.

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A novel solution is obtained to solve the rigid 3D registration problem, motivated by previous eigen-decomposition approaches. Different from existing solvers, the proposed algorithm does not require sophisticated matrix operations e.g. singular value decomposition or eigenvalue decomposition. Instead, the optimal eigenvector of the point cross-covariance matrix can be computed within several iterations. It is also proven that the optimal rotation matrix can be directly computed for cases without need of quaternion. The simple framework provides very easy approach of integer-implementation on embedded platforms. Simulations on noise-corrupted point clouds have verified the robustness and computation speed of the proposed method. The final results indicate that the proposed algorithm is accurate, robust and owns over 60% ∼ 80% less computation time than representatives. It has also been applied to real-world applications for faster relative robotic navigation.

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Preprocessing observation vectors to increase attitude estimation accuracy

Patera

2019

Advances in Space Research

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Optimal Attitude Determination from Vector Sensors Using Fast Analytical Singular Value Decomposition

Cited by 4 publications

References 20 publications

Fast Symbolic 3-D Registration Solution

Fast Symbolic 3-D Registration Solution

Rigid 3D Registration: A Simple Method Free of SVD and Eigen-Decomposition

Preprocessing observation vectors to increase attitude estimation accuracy

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