Variational Bayesian-Based Adaptive Error-State Kalman Filter With Application on LiDAR-Inertial Integrated Navigation System

In conventional integrated navigation systems, such as Kalman filter (KF), the statistical information of the process and measurement noise are assumed to be constant. However, in real applications, the process and measurement covariance matrices are unknown and time-varying due to vehicle dynamics, environmental conditions, and incomplete knowledge of filter statistical information. In this article, a variational Bayesian-based adaptive error-state KF (VB-ESKF) is proposed. By leveraging the versatility of the variational Bayesian framework, the filter effectively handles uncertainties and adaptively estimates the measurement noise covariance, resulting in improved accuracy and reliability. A LiDAR-Inertial state estimator based on VB-ESKF for real-time ego-motion estimation is proposed to provide robust and efficient navigation for ground vehicles. The tightly coupled LiDAR-Inertial navigation algorithm, based on the original ESKF and VB-ESKF, were implemented on the robot operating system (ROS) platform. The experimental results demonstrate significant advantages of the VB-ESKF in reducing root mean square error (RMSE), mean absolute error (MAE), and sensitivity to the nonoptimal process noise variance.