Fast RodFIter for Attitude Reconstruction from Inertial Measurements

TL;DR

This paper introduces a fast, computationally efficient version of the RodFIter method for attitude reconstruction from inertial measurements, maintaining high accuracy while enabling onboard implementation.

Contribution

It reformulates the Rodrigues vector integration using Chebyshev polynomials and truncation, significantly reducing computation complexity with guaranteed convergence.

Findings

Achieves faster attitude reconstruction with minimal accuracy loss

Validated through simulations demonstrating speed and precision

Enables onboard real-time attitude estimation

Abstract

Attitude computation is of vital importance for a variety of applications. Based on the functional iteration of the Rodrigues vector integration equation, the RodFIter method can be advantageously applied to analytically reconstruct the attitude from discrete gyroscope measurements over the time interval of interest. It is promising to produce ultra-accurate attitude reconstruction. However, the RodFIter method imposes high computational load and does not lend itself to onboard implementation. In this paper, a fast approach to significantly reduce RodFIter's computation complexity is presented while maintaining almost the same accuracy of attitude reconstruction. It reformulates the Rodrigues vector iterative integration in terms of the Chebyshev polynomial iteration. Due to the excellent property of Chebyshev polynomials, the fast RodFIter is achieved by means of appropriate truncation of Chebyshev polynomials, with provably guaranteed convergence. Moreover, simulation results validate the speed and accuracy of the proposed method.