Effect of Point Configurations on Parameter Estimation Analysis of Circles
Zhanfeng Song, Tao Fang, Paul M. Schonfeld, Jun Li · Journal of Surveying Engineering · 2021
The Fisher Information Matrix (FIM) determinant and the precision of the circle parameters are derived for generic configurations with n 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.