2022/01/22 by Farooq Aslam, Aslam, Farooq, Muhammad Farooq Haydar +1
Computer Science · Engineering · Mathematics · #Adaptive Control of Nonlinear Systems #Advanced Adaptive Filtering Techniques #Applied mathematics #Computer science #Control theory (sociology) #FOS: Electrical engineering #Filter (signal processing) #Filter design #Geometry #Inertial Sensor and Navigation #Kalman filter #Mathematics #Matrix (chemical analysis) #Nonlinear system #Orthogonal group #Physics #Pure mathematics #Quaternion #Rotation group SO #Rotation matrix #Statistics #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2201.08998
published in arXiv (Cornell University) (Cornell University)
arxiv created 2022/01/22 · openalex publication_date 2022/01/22 · arxiv updated 2022/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
The problem of H∞ filtering for attitude estimation using rotation matrices and vector measurements is studied. Starting from a storage function on the Special Orthogonal Group SO(3), a dissipation inequality is considered, and a deterministic nonlinear H∞ filter is derived which respects a given upper bound γ on the energy gain from exogenous disturbances and initial estimation errors to a generalized estimation error. The results are valid for all estimation errors which correspond to an angular error of less than π/2 radians in terms of the axis-angle representation. The approach builds on earlier results on attitude estimation, in particular nonlinear H∞ filtering using quaternions, and proposes a novel filter developed directly on SO(3). The proposed filter employs the same innovation term as the Multiplicative Extended Kalman Filter (MEKF), as well as a matrix gain updated in accordance with a Riccati-type gain update equation. However, in contrast to the MEKF, the proposed filter has an additional tuning gain, γ, which enables it to be more aggressive during transients. The filter is simulated for different conditions, and the results are compared with those obtained using the continuous-time quaternion MEKF and the Geometric Approximate Minimum Energy (GAME) filter. Simulations indicate competitive performance. In particular, the GAME filter has the best transient performance, followed by the proposed H∞ filter and the quaternion MEKF. All three filters have similar steady-state performance. Therefore, the proposed filter can be seen as a MEKF variant which achieves better transient performance without significant degradation in steady-state noise rejection.