提出一种新型递归推断算法，用于非高斯非线性状态空间模型的状态估计。
Recursive Entropic Variational Inference for Nonlinear State-Space Models
- 基于熵信任域更新的变分框架，结合动态一致性约束进行推断。
- 通过高斯-马尔可夫近似与傅里叶-埃尔米特矩匹配，实现低复杂度递归计算。
- 适用于复杂非线性系统，尤其适合需要高效在线推断的场景。
我们提出一类用于非线性、非高斯状态空间模型中状态估计的算法。方法基于变分拉格朗日形式，将贝叶斯推断转化为一系列受动态一致性约束的熵信任域更新。该框架导出一族前向-后向算法，其结构由变分后验的因子分解方式决定。通过聚焦高斯-马尔可夫近似，我们推导出计算复杂度较低的递归方案。对于一般非线性、非高斯模型，采用广义统计线性回归和傅里叶-埃尔米特矩匹配闭合递归关系。
原文摘要 · Abstract (English)
We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic consistency constraints. This framework gives rise to a family of forward-backward algorithms whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models, we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。