# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.09971