State estimation for nonlinear state space models is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear state space models (SSMs). DBF constructs new latent variables $h_t$ on a new latent (``fancy'') space and assimilates observations $o_t$. By (i) constraining the state transition on fancy space to be linear and (ii) learning a Gaussian inverse observation operator $q(h_t|o_t)$, posteriors always remain Gaussian for DBF. Quite distinctively, the structured design of posteriors provides an analytic formula for the recursive computation of posteriors without accumulating Monte-Carlo sampling errors over time steps. DBF seeks the Gaussian inverse observation operators $q(h_t|o_t)$ and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments show that DBF outperforms model-based approaches and latent assimilation methods in various tasks and conditions.

提出了用于非线性状态空间模型的深度贝叶斯滤波（DBF）方法，通过构建新的潜在变量并利用高斯逆观测算子进行数据同化，使得DBF的后验分布始终保持高斯性质，克服了采样误差积累的问题，并在各种任务和条件下优于基于模型和潜在同化方法。

深度贝叶斯滤波在贝叶斯可信数据同化中的应用