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首页> 外文期刊>IEEE Transactions on Automatic Control >Higher Order Nonlinear Complementary Filtering on Lie Groups
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Higher Order Nonlinear Complementary Filtering on Lie Groups

机译：李群上的高阶非线性互补滤波

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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.
机译：考虑了状态空间在李群上演化的系统的非线性观测器设计。所提出的方法与先前开发的非线性观测器相似，因为它涉及使用过程模型传播状态估计，并使用李群切线空间上的创新项校正传播的状态估计。在所提出的方法中，通过将基于切线空间解析的不变成本函数的梯度通过线性时不变系统来构造创新项。线性系统的引入通过允许更高阶的滤波，完成了将线性互补滤波器扩展到非线性李群观测器的任务。实际上，所提出的方法允许更大的设计自由度，并且通过适当选择线性滤波器，可以在特定带宽上滤波偏置和噪声。还应考虑在组速度测量中考虑恒定和谐波干扰的干扰观测器。证明了在所需平衡点附近的局部渐近稳定性。在姿势估计的背景下，给出了一个数值示例，该示例演示了观察者的理想特性。

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