# Multi-kernel Correntropy-based Orientation Estimation of IMUs: Gradient Descent Methods

arXiv: https://arxiv.org/abs/2304.06548 · HTML: https://mlsanity.com/paper/2304.06548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 53 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 5 of 5)

- [Using Inertial Sensors for Position and Orientation Estimation](https://mlsanity.com/paper/1704.06053/) (2017)
- [Generalized Kalman Smoothing: Modeling and Algorithms](https://mlsanity.com/paper/1609.06369/) (2016)
- [Robustness analysis of a Maximum Correntropy framework for linear regression](https://mlsanity.com/paper/1703.04829/) (2017)
- [Newton-based maximum likelihood estimation in nonlinear state space models](https://mlsanity.com/paper/1502.03655/) (2015)
- [A Fast and Robust Algorithm for Orientation Estimation using Inertial Sensors](https://mlsanity.com/paper/1910.00463/) (2019)

## Abstract (arXiv)

This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors.