Effect of Point Configurations on Parameter Estimation Analysis of Circles
Publication: Journal of Surveying Engineering
Volume 147, Issue 3
Abstract
The Fisher Information Matrix (FIM) determinant and the precision of the circle parameters are derived for generic configurations with data points. The conditions for maximizing the FIM determinant are examined, and analysis shows that an infinite number of point configurations exist to maximize the FIM determinant. A collinear point configuration is proposed to obtain the highest precision of the radius, as do the configurations with the maximum FIM determinant. Moreover, theoretical analysis and the Monte Carlo method are employed to reveal that the highest precision of the parameter estimation is achieved synchronously with the maximum FIM determinant. When points are limited along an arc, the distribution ratio sequence (DRS) is designed to describe point configurations. Experiments show that the DRS of the maximum FIM determinant generally outperforms other arbitrary ones when points are limited along a certain arc.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant No. 51678574). The first author thanks the China Scholarship Council (Grant No. 201706375006) for financially supporting his studies at the University of Maryland.
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Journal of Surveying Engineering
Volume 147 • Issue 3 • August 2021
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© 2021 American Society of Civil Engineers.
History
Received: Sep 27, 2020
Accepted: Mar 30, 2021
Published online: May 19, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 19, 2021
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