Identification of the inertia matrix of a rotating body based on errors-in-variables models

Abstract

This paper proposes a procedure for identifying the inertia matrix of a rotating body. The procedure based on Euler's equation governing rotational motion assumes errors-in-variables models in which all measurements, torque as well as angular velocities, are corrupted by noises. In order for consistent estimation, we introduce an extended linear regression model by augmenting the regressors with constants and the parameters with noise-contributed terms. A transformation, based on low-pass filtering, of the extended model cancels out angular acceleration terms in the regressors. Applying the method of least correlation to the model identifies the elements of the inertia matrix. Analysis shows that the estimates converge to the true parameters as the number of samples increases to infinity. Monte Carlo simulations demonstrate the performance of the algorithm and support the analytical consistency. Copyright © 2009 John Wiley & Sons, Ltd.