# Attitude Reconstruction from Inertial Measurements: QuatFIter and Its Comparison with RodFIter

## TL;DR

This paper introduces QuatFIter, a quaternion-based attitude reconstruction method derived from RodFIter, demonstrating comparable accuracy but improved computational efficiency through polynomial approximation and truncation techniques.

## Contribution

It extends RodFIter to quaternion representation, showing equivalence to existing methods and enhancing efficiency with Chebyshev polynomial techniques.

## Key findings

- QuatFIter achieves similar accuracy to RodFIter.
- QuatFIter is approximately twice as fast computationally.
- Convergence of QuatFIter is slightly slower with more iterations.

## Abstract

RodFIter is a promising method of attitude reconstruction from inertial measurements based on the functional iterative integration of Rodrigues vector. The Rodrigues vector is used to encode the attitude in place of the popular rotation vector because it has a polynomial-like rate equation and could be cast into theoretically sound and exact integration. This paper further applies the approach of RodFIter to the unity-norm quaternion for attitude reconstruction, named QuatFIter, and shows that it is identical to the previous Picard-type quaternion method. The Chebyshev polynomial approximation and truncation techniques from the RodFIter are exploited to speed up its implementation. Numerical results demonstrate that the QuatFIter is comparable in accuracy to the RodFIter, although its convergence rate is relatively slower with respect to the number of iterations. Notably, the QuatFIter has about two times better computational efficiency, thanks to the linear quaternion kinematic equation.

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Source: https://tomesphere.com/paper/1901.03468