Calibration Method of Orthogonally Splitting Imaging Pose Sensor Based on KDFcmPUM

Area of Science:

• Computational Mathematics
• Numerical Analysis
• Data Science

Background:

• Radial basis function (RBF) interpolation faces computational challenges with large scattered datasets due to dense matrix formation.
• Existing methods struggle to efficiently handle the scale and complexity of such problems.

Purpose of the Study:

• To propose a novel Kernel Fuzzy Clustering-based Partition of Unity Method (KDFcmPUM) to overcome the dense matrix problem in RBF interpolation.
• To enhance clustering accuracy and achieve partition of unity for improved interpolation performance.
• To apply and validate the KDFcmPUM for mathematical modeling and calibration of orthogonally splitting imaging pose sensors.

Main Methods:

• Development of KDFcmPUM integrating a kernel fuzzy clustering algorithm for improved accuracy and partition of unity.
• Utilization of local compact support RBF for constructing weight functions and local interpolation expressions.
• Construction of the global expression using the derived weight functions and local expressions.

Main Results:

• Successful application of KDFcmPUM to an orthogonally splitting imaging pose sensor for mathematical modeling.
• Achieved calibration and test accuracy of ±0.1 mm.
• Demonstrated a reduction of at least 4% in the number of operations compared to existing methods.

Conclusions:

• The KDFcmPUM is an effective method for solving the dense matrix problem in RBF interpolation with large scattered data.
• The method offers improved accuracy and computational efficiency, as evidenced by the imaging pose sensor application.
• KDFcmPUM shows significant potential for applications requiring precise scattered data interpolation.