Adaptive Invariant Extended Kalman Filter with Noise Covariance Tuning for Attitude Estimation

TL;DR

This paper addresses the challenge of attitude estimation using quaternion-based adaptive right invariant extended Kalman filtering (RI-EKF) that integrates data from inertial and magnetometer sensors, and applies the expectation-maximization algorithm to estimate noise covariance, exploiting RI-EKF symmetry properties.

Abstract

Attitude estimation is crucial in aerospace engineering, robotics, and virtual reality applications, but faces difficulties due to nonlinear system dynamics and sensor limitations. This paper addresses the challenge of attitude estimation using quaternion-based adaptive right invariant extended Kalman filtering (RI-EKF) that integrates data from inertial and magnetometer sensors. Our approach applies the expectation-maximization (EM) algorithm to estimate noise covariance, exploiting RI-EKF symmetry properties. We analyze the adaptive RI-EKF's stability, convergence, and accuracy, validating its performance through simulations and comparison with the left invariant EKF. Monte Carlo simulations validate the effectiveness of our noise covariance estimation technique across various window lengths.

Figures (4)

• Figure 1: Elements of the Kalman gain matrix $K_k$ for the LI-EKF and RI-EKF.
• Figure 2: Convergence of Error Norm for the RI-EKF over different initial orientations.
• Figure 3: Gyroscope noise covariance estimation.
• Figure 4: Accelerometer and magnetometer noise covariance estimation.