Estimating Variance–Covariance Matrix of the Parameters of a Fitted Triaxial Ellipsoid

Abstract

Least-squares (LS) techniques have been a frequent choice advocated by a plethora of engineers for modeling problems requiring a unique solution based on sets of redundant observations perturbed by random noise. In this paper, several versions of LS procedures using the general quadric polynomial equation as the math model are reviewed and applied to a triaxial ellipsoid fitting exercise. The coefficients of this polynomial are then transformed into the nine parameters defining the spatial properties of the ellipsoid: semiaxes, coordinates of the origin, and rotation angles. Finally, a novel methodology requiring eigentheory is introduced to complete the determination of the variance–covariance matrices of these parameters.