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.

翻译：本文提出了两种用于惯性测量单元（IMU）姿态估计的高效计算算法：基于相关熵的梯度下降（CGD）和基于相关熵的解耦姿态估计（CDOE）。传统方法如梯度下降（GD）和解耦姿态估计（DOE）依赖于均方误差（MSE）准则，使其易受外部加速度和磁干扰的影响。为解决此问题，我们证明当噪声服从一类重尾分布时，多核相关熵损失（MKCL）是最大似然估计（MLE）的最优目标函数。在某些情况下，即使存在任意大的异常值，MKCL的估计误差也有界。通过用MKCL替代标准MSE代价函数，我们开发了CGD和CDOE算法。通过在不同场景下与现有算法进行比较，评估了我们提出方法的有效性。实验结果表明，我们提出的方法（CGD和CDOE）在面临外部加速度和磁干扰时，性能优于传统方法（GD和DOE）。此外，新算法的计算复杂度明显低于基于卡尔曼滤波的方法，使其适用于低成本微处理器的应用场景。