Iterative Robust Ellipsoid Fitting Based on M-Estimator With Geometry Radius Constraint

Abstract

The ellipsoid fitting technique has been popularly used in many application scenarios, especially in triaxial sensor calibration in recent years. The conventional method to achieve ellipsoid fitting is the pseudo-inverse technique with algebraic constraints to obtain proper fitting results. This technique ensures the least mean square (LMS) error relative to all measured data and prevents trivial solutions. However, this approach lacks robustness against outliers resulting in nonideal fitting performance in real calibration situations. The M-estimator technique with several robust cost functions is adopted and applied in this research to attenuate the outlier’s effect to offer a more accurate fitting performance. In contrast, the constraint with geometric meaning is also applied and examined to prevent trivial solutions. These two methods are achieved by using the iterative constrained gradient descent (G.D.) method to approach the proper ellipsoid fitting. The performances are validated through synthesis and real measured data. Through calibrated experiments, the proposed methods are found to be able to increase robustness against outliers and prevent parameters of ellipsoid degeneration toward trivial solutions.