Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation

Abstract

This paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of the Bayes–Sard quadrature transformation, we first established a Bayesian estimator on matrix Lie groups for system measurements in Euclidean spaces or Lie groups. The estimator was then employed to develop a generalized Bayes–Sard cubature Kalman filter on matrix Lie groups that considers additional uncertainties brought by integration errors and contains two variants. We also built on the maximum likelihood principle, and an adaptive version of the proposed filter was derived for better algorithm flexibility and more precise filtering results. The proposed filters were applied to the quaternion attitude estimation problem. Monte Carlo numerical simulations supported that the proposed filters achieved better estimation quality than that of other Lie group filters in the mentioned studies.