We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

翻译：我们提出了一种新颖、可证明鲁棒且具有闭式解的贝叶斯更新规则，用于在存在异常值和错误指定的测量模型时对状态空间模型进行在线滤波。该方法将广义贝叶斯推断与扩展卡尔曼滤波、集合卡尔曼滤波等滤波方法相结合：利用广义贝叶斯推断保证鲁棒性，通过滤波方法确保非线性模型的计算效率。与基于变分贝叶斯等其他鲁棒滤波方法相比，该方法在显著降低计算成本的同时，性能持平或更优。我们在包含异常值测量的多种滤波问题中进行了实验验证（如目标跟踪、高维混沌系统的状态估计及神经网络在线学习），结果证实了其有效性。