In this paper, we consider an estimation problem of invariant nonlinear systems subject to dynamic additive disturbances. We identify two sets of sufficient conditions that preserve the invariant properties of the systems under the disturbances. We apply the conditions to a unicycle model under linear dynamic disturbances and design two different Invariant Extended Kalman filters (IEKFs). Both IEKFs estimate the state of the unicycle and the disturbances based on position measurements. We also propose a correction to the IEKF covariances to better represent uncertainties in the invariant frame. The benefit of including the covariance correction and the performances of the two IEKF designs are demonstrated through Monte-Carlo simulations.

在本文中，我们考虑具有动态加性扰动的不变非线性系统的估计问题。我们确定了两组足以保持扰动下系统不变性质的条件。我们将条件应用于线性动态扰动下的单轮模型，并设计两个不同的不变扩展卡尔曼滤波器（IEKF）。两个IEKF都根据位置测量值估算单轮车的状态和干扰。我们还建议对IEKF协方差进行校正，以更好地表示不变框架中的不确定性。通过蒙特卡洛仿真证明了包括协方差校正和两种IEKF设计性能的好处。