# Attitude Reconstruction from Inertial Measurement: Mitigating Runge Effect for Dynamic Applications

arXiv: https://arxiv.org/abs/2107.04722 · HTML: https://mlsanity.com/paper/2107.04722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Interpretable System Identification and Long-term Prediction on Time-Series Data](https://mlsanity.com/paper/2303.01193/) (2023)

## Abstract (arXiv)

Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions.