Attitude estimation based on observation vector inertia

Abstract

A new method of attitude estimation is developed based on the inertia matrices associated with the mass distributions defined by reference vectors in the inertial frame and observation vectors in the body frame. Each reference vector and associated observation vector defines the location of an adjustable point mass to create a related inertia tensor. The inertia matrices from each reference vector are combined to form the total inertia tensor in the inertial frame. The total inertia tensor in the body frame is found in a similar fashion using observation vectors. The eigenvalues of the reference frame inertia tensor are identical to the eigenvalues of the body frame inertia tensor, since the eigenvalues are independent of reference frame. Diagonalization of each inertia tensor provides not only the eigenvalues and eigenvectors of the respective matrices, but also the associated transformations from inertial and body frames to the diagonal frame. Combining the transformation from body frame to diagonal frame with the transformation from diagonal frame to inertial frame provides the body attitude estimate. The related coordinate frames are implicitly orthogonal and the attitude solution does not require iteration. This method is similar to the TRIAD method but unlike the TRIAD method which can only use two vectors, this method can make use of any number of observation vectors. In addition, the masses associated with each observation vector can be adjusted to improve estimation accuracy and in many cases provide the optimal attitude estimate. Numerical results for previously published test cases are presented to demonstrate attitude estimation accuracy.