论文标题
非线性$ h _ {\ infty} $在特殊正交组$ so（3）$使用矢量方向上过滤
Nonlinear $H_{\infty}$ Filtering on the Special Orthogonal Group $SO(3)$ using Vector Directions
论文作者
论文摘要
研究了$ h _ {\ infty} $过滤使用旋转矩阵和向量测量值的态度估算的问题。从特殊正交组$上的存储功能开始，因此考虑了耗散不平等，并得出了确定性的非线性$ h _ {\ infty} $滤波器，这尊重给定的上限$γ$从外源性干扰中获得的能量$γ$，以及对广义估计错误的初始估计错误。对于所有估计误差，结果对应于轴 - 角度表示的所有估计误差小于$π/2 $弧度。该方法基于早期的态度估计结果，尤其是使用Quaternions的非线性$ H _ {\ infty} $过滤，并提出了直接在$ SO（3）$上开发的新颖过滤器。所提出的过滤器采用与乘法扩展的Kalman过滤器（MEKF）相同的创新项，以及根据Riccati-Type增益更新方程式更新的矩阵增益。但是，与MEKF相比，提出的过滤器具有额外的调谐增益，即$γ$，这使其在瞬态过程中更具侵略性。对过滤器进行模拟，并将结果与使用连续时间Quaternion MEKF和几何最小能量（游戏）过滤器获得的结果进行比较。模拟表示竞争性能。特别是，游戏过滤器具有最佳的瞬态性能，然后是建议的$ h _ {\ infty} $过滤器和Quaternion MEKF。这三个过滤器都具有相似的稳态性能。因此，提出的过滤器可以看作是MEKF变体，可以在稳态噪声排斥中实现更好的瞬态性能而没有显着降解。
The problem of $H_{\infty}$ 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 $H_{\infty}$ 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 $H_{\infty}$ 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 $H_{\infty}$ 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.
