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

Deep Bayesian Filter for Bayes-faithful Data Assimilation

Motivated by the maneuvering target tracking with sensors such as radar and
sonar, this paper considers the joint and recursive estimation of the dynamic
state and the time-varying process noise covariance in nonlinear state space
models. Due to the nonlinearity of the models and the non-conjugate prior, the
state estimation problem is generally intractable as it involves integrals of
general nonlinear functions and unknown process noise covariance, resulting in
the posterior probability distribution functions lacking closed-form solutions.
This paper presents a recursive solution for joint nonlinear state estimation
and model parameters identification based on the approximate Bayesian inference
principle. The stochastic search variational inference is adopted to offer a
flexible, accurate, and effective approximation of the posterior distributions.
We make two contributions compared to existing variational inference-based
noise adaptive filtering methods. First, we introduce an auxiliary latent
variable to decouple the latent variables of dynamic state and process noise
covariance, thereby improving the flexibility of the posterior inference.
Second, we split the variational lower bound optimization into conjugate and
non-conjugate parts, whereas the conjugate terms are directly optimized that
admit a closed-form solution and the non-conjugate terms are optimized by
natural gradients, achieving the trade-off between inference speed and
accuracy. The performance of the proposed method is verified on radar target
tracking applications by both simulated and real-world data.

本文研究非线性状态空间模型中动态状态和动态噪声协方差的联合和递归估计问题，提出了一种基于近似贝叶斯推断原理的非线性状态估计和模型参数识别的递归解决方案。方法基于随机搜索变分推断，通过引入辅助潜变量和优化共轭和非共轭项实现了推断速度和准确度的平衡，通过仿真和实际数据的雷达跟踪应用验证了方法的性能。