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：本文针对存在异常值和测量模型误设的状态空间模型在线滤波问题，提出了一种新颖的、可证明具有鲁棒性且具有闭式解的贝叶斯更新规则。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。我们利用广义贝叶斯推断证明其鲁棒性，并借助非线性滤波方法确保非线性模型情况下的计算效率。本方法在计算成本显著降低的同时，其性能达到或超越了其他鲁棒滤波方法（例如基于变分贝叶斯的方法）。我们在包含异常值测量的多种滤波问题上进行了实证验证，包括目标跟踪、高维混沌系统的状态估计以及神经网络的在线学习。