State-space models (SSMs) provide a flexible framework for modelling time series data, but their reliance on Gaussian error assumptions makes them highly sensitive to outliers. We propose a robust estimation method, ROAMS, that mitigates the influence of additive outliers by introducing shift parameters at each timepoint in the observation equation of the SSM. These parameters allow the model to attribute non-zero shifts to outliers while leaving clean observations unaffected. ROAMS then enables automatic outlier detection, through the addition of a penalty term on the number of flagged outlying timepoints in the objective function, and simultaneous estimation of model parameters. We apply the method to robustly estimate SSMs on both simulated data and real-world animal location-tracking data, demonstrating its ability to produce more reliable parameter estimates than classical methods and other benchmark methods. In addition to improved robustness, ROAMS offers practical diagnostic tools, including BIC curves for selecting tuning parameters and visualising outlier structure. These features make our approach broadly useful for researchers and practitioners working with contaminated time series data.

翻译：状态空间模型（SSMs）为时间序列数据建模提供了一个灵活的框架，但其对高斯误差假设的依赖使其对离群值高度敏感。我们提出了一种鲁棒估计方法ROAMS，通过在SSM观测方程中每个时间点引入漂移参数来减轻加性离群值的影响。这些参数允许模型将非零漂移归因于离群值，同时保持清洁观测不受影响。ROAMS通过在目标函数中对标记离群时间点数量添加惩罚项，实现了自动离群值检测与模型参数的同步估计。我们将该方法应用于模拟数据和真实世界动物位置追踪数据上的SSM鲁棒估计，证明其相比经典方法及其他基准方法能产生更可靠的参数估计。除提升鲁棒性外，ROAMS还提供了实用的诊断工具，包括用于选择调优参数的BIC曲线和离群值结构可视化。这些特性使得我们的方法对处理受污染时间序列数据的研究人员和实践者具有广泛实用性。