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Convergence analysis of non-linear filtering based on cubature Kalman filter

机译:基于库尔曼卡尔曼滤波的非线性滤波的收敛性分析

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摘要

This study analyses the stability of cubature Kalman filter (CKF) for non-linear systems with linear measurement. The certain conditions to ensure that the estimation error of the CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Since adaptation law has a very important role in convergence, fuzzy logic is proposed to improve the versatility of the proposed adaptive noise covariance. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the modified CKF is compared to the CKF in two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF, while the MCKF is successfully able to estimate the states. In addition, the superiority of MCKF that uses fuzzy adaptation rules is shown.
机译:这项研究分析了带有线性测量的非线性系统的库尔曼卡尔曼滤波器(CKF)的稳定性。证明了确保CKF的估计误差保持有界的某些条件。然后,研究了过程噪声协方差的影响,并提出了一种自适应的过程噪声协方差来处理较大的估计误差。由于自适应定律在收敛中具有非常重要的作用,因此提出了模糊逻辑来提高所提出的自适应噪声协方差的通用性。因此,开发了改进的CKF(MCKF)以增强状态估计的稳定性和准确性。在两个案例研究中,将修改后的CKF的性能与CKF进行了比较。仿真结果表明,较大的估计误差可能会导致CKF不稳定,而MCKF能够成功估计状态。此外,显示了使用模糊自适应规则的MCKF的优越性。

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