Robust Attitude Estimation with Quaternion Left-Invariant EKF and Noise Covariance Tuning

TL;DR

This work tackles attitude estimation under unknown and time-varying noise by integrating a quaternion left-invariant EKF (LI-EKF) with an iterative EM-based adaptive scheme for estimating process and measurement noise covariances. The method leverages a multiplicative error formulation on quaternions and a left-invariant structure to improve consistency and convergence, while the EM procedure (with RTS smoothing) updates Q and R online. Simulation results show the covariance estimates converge toward their true values and attitude estimates remain accurate across various initializations and noise conditions. The approach offers a robust solution for aerospace, robotics, and autonomous systems requiring reliable attitude estimation with unknown noise characteristics.

Abstract

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman filter (LI-EKF) for attitude estimation, integrated with an adaptive noise covariance estimation algorithm. By employing an iterative expectation-maximization (EM) approach, the filter can effectively estimate both process and measurement noise covariances. Extensive simulations demonstrate the superiority of the proposed method in terms of attitude estimation accuracy and robustness to initial parameter misspecification. The adaptive LI-EKF's ability to adapt to time-varying noise characteristics makes it a promising solution for various applications requiring reliable attitude estimation, such as aerospace, robotics, and autonomous systems.

Figures (2)

• Figure 1: Convergence of the log-likelihood function.
• Figure 2: Scatter plot of Q and R estimates, + denotes the true values.