Shilei Li

Shilei Li, Lijing Li, Dawei Shi et al.

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.

Shilei Li, Dawei Shi, Hao Yu et al.

Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical applications, both process and measurement noise can be influenced by outliers, be time-varying, or both. In this work, we propose a variational robust Kalman filter, built on a Student's $t$-distribution induced loss function and variational inference, and solved in a computationally efficient manner. We demonstrate that robustness can be understood as a prerequisite for adaptivity, making it possible to merge the above two competing goals into a single framework through a probabilistic switching rule. Additionally, our proposed filter can recover conventional KF, robust KF, and adaptive KF by tuning parameters, and can suppress both the imperfect process and measurement noise, enabling it to perform superiorly in complex noise environments. Simulations verify the effectiveness of the proposed method.

Wanlei Li, Zichang Chen, Shilei Li et al.

State estimation for legged robots remains challenging because legged odometry generally suffers from limited observability and therefore depends critically on measurement constraints to suppress drift. When exteroceptive sensors are unreliable or degraded, such constraints are mainly derived from proprioceptive measurements, particularly contact-related leg kinematics information. However, most existing proprioceptive odometry methods rely on an idealized point-contact assumption, which is often violated during real locomotion. Consequently, the effectiveness of proprioceptive constraints may be significantly reduced, resulting in degraded estimation accuracy. To address these limitations, we propose an interacting multiple model (IMM)-based proprioceptive odometry framework for legged robots. By incorporating multiple contact hypotheses within a unified probabilistic framework, the proposed method enables online mode switching and probabilistic fusion under varying contact conditions. Extensive simulations and real-world experiments demonstrate that the proposed method achieves superior pose estimation accuracy over state-of-the-art methods while maintaining comparable computational efficiency.