Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as geoscience and meteorology. Despite their inability to produce the true posterior distribution for nonlinear systems, their robustness and capacity for state tracking are noteworthy. In contrast, Particle filters yield the correct distribution in the ensemble limit but require substantially larger ensemble sizes than ensemble-based filters to maintain stability in higher-dimensional spaces. It is essential to transcend traditional Gaussian assumptions to achieve realistic quantification of uncertainties. One approach involves the hybridisation of filters, facilitated by tempering, to harness the complementary strengths of different filters. A new adaptive tempering method is proposed to tune the underlying schedule, aiming to systematically surpass the performance previously achieved. Although promising numerical results for certain filter combinations in toy examples exist in the literature, the tuning of hyperparameters presents a considerable challenge. A deeper understanding of these interactions is crucial for practical applications.

翻译：数据同化算法将数值模型模拟的先验信息与观测数据相结合。基于集合的滤波器作为当前最先进的方法，被广泛应用于地球科学和气象学等领域的大规模估计任务。尽管它们无法为非线性系统生成真实的后验分布，但其鲁棒性和状态跟踪能力值得关注。相比之下，粒子滤波器在集合极限下能产生正确的分布，但需要比基于集合的滤波器大得多的集合规模以维持高维空间中的稳定性。必须超越传统的高斯假设才能实现不确定性的现实量化。一种方法是通过调温实现滤波器的混合，以利用不同滤波器的互补优势。本文提出了一种新的自适应调温方法来调整基础调度方案，旨在系统性地超越先前实现的性能。尽管文献中针对玩具示例的某些滤波器组合已显示出有希望的数值结果，但超参数的调整仍面临重大挑战。深入理解这些相互作用对于实际应用至关重要。