This paper presents a novel approach for nonlinear assimilation called score-based sequential Langevin sampling (SSLS) within a recursive Bayesian framework. SSLS decomposes the assimilation process into a sequence of prediction and update steps, utilizing dynamic models for prediction and observation data for updating via score-based Langevin Monte Carlo. An annealing strategy is incorporated to enhance convergence and facilitate multi-modal sampling. The convergence of SSLS in TV-distance is analyzed under certain conditions, providing insights into error behavior related to hyper-parameters. Numerical examples demonstrate its outstanding performance in high-dimensional and nonlinear scenarios, as well as in situations with sparse or partial measurements. Furthermore, SSLS effectively quantifies the uncertainty associated with the estimated states, highlighting its potential for error calibration.

翻译：本文提出了一种名为基于分数的序贯朗之万采样（SSLS）的非线性同化新方法，该方法基于递归贝叶斯框架。SSLS将同化过程分解为一系列预测和更新步骤，利用动态模型进行预测，并通过基于分数的朗之万蒙特卡洛方法结合观测数据进行更新。该方法引入了退火策略以增强收敛性并促进多模态采样。在特定条件下，分析了SSLS在TV距离上的收敛性，从而揭示了与超参数相关的误差行为。数值算例表明，该方法在高维非线性场景以及稀疏或部分观测情况下均表现出卓越的性能。此外，SSLS能有效量化与估计状态相关的不确定性，突显了其在误差校准方面的潜力。