在李群上进行高阶非线性互补滤波
Higher-Order Nonlinear Complementary Filtering on Lie Groups
AI总结：
本文提出在李群状态空间上设计非线性观测器的方法，通过在切空间上引入线性系统实现高阶滤波，增强设计自由度并能滤除特定带宽的偏置和噪声。
摘要：
对于状态空间在李群上演化的系统，本文考虑非线性观测器设计。所提方法与之前开发的非线性观测器类似，通过过程模型传播状态估计，并在李群的切空间上使用创新项进行校正。在所提方法中，创新项通过将不变成本函数的梯度（以切空间基为基）传递通过线性时不变系统来构建。引入线性系统完成了将线性互补滤波扩展到非线性李群观测器的延伸，允许高阶滤波。实际上，所提方法允许更大的设计自由度，通过适当选择线性滤波器，能够对特定带宽内的偏置和噪声进行滤波。还考虑了考虑常数和调谐扰动的干扰观测器。在期望平衡点附近展示了局部渐近稳定性。在姿态估计背景下展示了体现观测器优良性质的数值示例。
英文摘要：
Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model and corrects the propagated state estimate using an innovation term on the tangent space of the Lie group. In the proposed method, the innovation term is constructed by passing the gradient of an invariant cost function, resolved in a basis of the tangent space, through a linear time-invariant system. The introduction of the linear system completes the extension of linear complementary filters to nonlinear Lie group observers by allowing higher-order filtering. In practice, the proposed method allows for greater design freedom and, with the appropriate selection of the linear filter, the ability to filter bias and noise over specific bandwidths. A disturbance observer that accounts for constant and harmonic disturbances in group velocity measurements is also considered. Local asymptotic stability about the desired equilibrium point is demonstrated. A numerical example that demonstrates the desirable properties of the observer is presented in the context of pose estimation.
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