Abstract In this study, a novel RCDKF 1 is proposed for nonlinear plants. The system under consideration is a comprehensive case where the norm bounded uncertainties are supposed in both the state and output equations. Since the filtering methodology has been suggested based on the Stirling formula, it requires no derivative or Jacobian matrix computations. Furthermore, the mean value of uncertainties has been eliminated in the development of the filter structure. Different types of uncertainties are incorporated in the standard formulation of CDKF and it is demonstrated that the upper bound of covariance matrices can be derived according to them. In contrast to the similar works, the stability of the proposed filtering strategy is proved by the Lyapunov theory and the upper bound of state estimation error covariance is found for all admissible uncertainties. To demonstrate the performance of the introduced estimation algorithm, it will be evaluated on the attitude determination system of a three-axis satellite including a star camera and gyro sensor. The simulation results of the proposed filter are compared with the conventional CDKF, 2 NRF, 3 EKF 4 and PF 5 and the better efficiency of the developed method is established.

中文翻译：

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存在不确定性和未知测量误差的鲁棒中心差分卡尔曼滤波器的设计

摘要 在这项研究中，提出了一种用于非线性设备的新型 RCDKF 1。所考虑的系统是一个综合情况，其中在状态方程和输出方程中都假设有范数有界不确定性。由于过滤方法是基于斯特林公式提出的，因此不需要导数或雅可比矩阵计算。此外，在滤波器结构的开发中消除了不确定性的平均值。CDKF 的标准公式中包含了不同类型的不确定性，并且证明可以根据它们导出协方差矩阵的上限。与同类作品相比，Lyapunov 理论证明了所提出的滤波策略的稳定性，并找到了所有可允许的不确定性的状态估计误差协方差的上限。为了演示引入的估计算法的性能，将在包括星相机和陀螺仪传感器的三轴卫星姿态确定系统上进行评估。将所提出的滤波器的仿真结果与传统的 CDKF、2 NRF、3 EKF 4 和 PF 5 进行比较，并建立了所开发方法的更好效率。