Attitude Quaternion Estimation Using a Spectral Perturbation Approach

TL;DR

This paper introduces a spectral perturbation approach for attitude quaternion estimation, enabling high-accuracy, recursive calculations that overcome numerical challenges of existing methods, beneficial for embedded systems like spacecraft.

Contribution

It presents an analytical and recursive method for attitude quaternion estimation that improves accuracy and numerical stability over traditional spectral decomposition techniques.

Findings

High-accuracy quaternion estimation achieved

Recursive calculation of maximum-likelihood quaternion demonstrated

Numerical difficulties in existing methods addressed

Abstract

All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral perturbation approach, we show it is possible to analytically estimate the attitude quaternion to high accuracy and recursively calculate the maximum-likelihood attitude quaternion to arbitrary numerical precision. Analytic or recursive estimation removes several numerical difficulties which are inherent to state-of-the-art algorithms, suggesting our results may substantially benefit high-frequency and limited memory embedded software implementations, such as those commonly used on spacecraft computers.