For continuous-discrete filtering with unpredictable approximation errors, by proposing the novel stochastic feedback scheme, this note elaborates a closed-loop adaptive Kalman filter for nonlinear continuous-discrete systems. In conventional filters, unknown approximation errors might arise due to the integration/discretization and linearization of continuous model, and ruin the optimality of Kalman theory. As the main contribution of this note, the stochastic feedback based covariance adaption scheme does not require the approximation steps; instead, the posteriori sequence is mined as a feedback to adapt the priori error covariance, so that the unpredictable errors and costly calculations can be reduced or controlled in the novel closed-loop filtering structure. The new approach's advantages in computational cost, adaptability, and accuracy have been demonstrated by the numerical simulations.

中文翻译：

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非线性连续离散系统的基于随机反馈的卡尔曼滤波器

对于具有不可预测逼近误差的连续离散滤波，本文通过提出新颖的随机反馈方案，阐述了一种用于非线性连续离散系统的闭环自适应卡尔曼滤波器。在传统滤波器中，由于连续模型的积分/离散化和线性化可能会产生未知的近似误差，从而破坏卡尔曼理论的最优性。作为本笔记的主要贡献，基于随机反馈的协方差自适应方案不需要近似步骤；相反，后验序列被挖掘为反馈以适应先验误差协方差，从而在新型闭环滤波结构中可以减少或控制不可预测的误差和昂贵的计算。新方法在计算成本、适应性、