This paper presents a post-Bayesian approach to online filtering in nonlinear state-space models, capable of avoiding over-confident inferences in settings where either the dynamical model, the measurement model, or both, could be misspecified. This is addressed using predictively oriented (PrO) posteriors, an emerging paradigm in which learning (i.e., posterior concentration) occurs if and only if the overall model is well-specified, without strict adherence to Bayes' theorem. As the characterisation of PrO posteriors is challenging, our main technical contribution is a fast approximate linear-Gaussian update procedure, analogous to an (iterated) extended Kalman filter. The methodology, which we call EKF-PrO, has no tunable hyper-parameters and has a computational cost comparable to that of existing filtering methods. Performance is empirically assessed on a range of linear and non-linear applications, in which the state-space model is systematically misspecified.

翻译：本文提出了一种后贝叶斯方法，用于非线性状态空间模型中的在线滤波，能够在动力学模型、测量模型或两者均存在错误设定时避免过度自信的推断。该问题通过面向预测的后验分布来解决，这是一种新兴范式，其中学习（即后验集中）仅在整体模型被良好设定的情况下发生，而无需严格遵循贝叶斯定理。由于面向预测后验的表征具有挑战性，本文的主要技术贡献在于提出了一种快速近似的线性-高斯更新过程，类似于（迭代）扩展卡尔曼滤波。我们将该方法称为EKF-PrO，其无可调节超参数，计算成本与现有滤波方法相当。通过一系列线性与非线性应用（其中状态空间模型被系统性错误设定）对性能进行了实证评估。