Homotopic Gaussian Mixture Filtering for Applied Bayesian Inference

• 成果类型: Article
• 署名作者: Craft, Kyle J.; DeMars, Kyle J.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3530878
• 发表日期: 2025
• 页码: 4608-4623
• 关键词: Bayes methods; Probability density function; accuracy; vectors; mathematical models; iterative methods; Taylor series; Measurement uncertainty; MANIFOLDS; Transforms; Bayesian inference; Gaussian mixture (GM) model; nonlinear filtering

摘要

Bayes' rule, although a powerful framework for performing state estimation, is often intractable for real-world, nonlinear dynamic systems. As a result, estimation algorithms typically rely on a simplifying assumption, such as the linearity of the measurement model or Gaussianity of the likelihood function. For nonlinear, non-Gaussian systems, these approximations can introduce statistical inconsistencies into the underlying estimator. To mitigate approximation errors, a homotopic scheme is proposed for Bayesian inference. The approach partitions Bayes' rule into smaller, incremental corrections, over which linear and/or Gaussian assumptions are more accurate. The incremental update is limited to zero, yielding a system of first-order differential equations governing the update from prior to posterior for the weights, means, and covariances of a finite Gaussian mixture approximation. The proposed method is shown to be generalizable to both non-Gaussian likelihoods and likelihoods with non-Euclidean support. The homotopic filter is applied to a dynamic state estimation scenario and noticeable improvements over traditional Bayesian filtering techniques (e.g., the unscented Kalman filter and conventional Gaussian mixture filtering) are observed.