State-space models (SSMs) are a broad class of probabilistic models for dynamical systems with many applications in engineering and science. Bayesian filtering is analytically tractable only in the linear-Gaussian setting, where the Kalman filter yields exact posterior distributions. For nonlinear or non-Gaussian SSMs, approximations are required. Two prominent families of approximate methods are Gaussian sum filters (GSFs), which rely on local Gaussian approximations and numerical integration schemes, and particle filters (PFs), which use sequential Monte Carlo sampling. Despite their success, GSFs can suffer from numerical instabilities and severe failures in strongly nonlinear regimes, while PFs are flexible and robust but often demand substantial computational resources to achieve accurate estimates. In this work, we propose the Augmented Gaussian Sum Filter (AGSF), a novel filtering framework that unifies GSFs and PFs through an augmented Gaussian approximation parameterized by latent variables and tunable covariance parameters. By adjusting these covariances, the AGSF interpolates continuously between GSF-like and PF-like behavior, recovering both as special cases. Building on this view, we develop an adaptive AGSF that automatically shifts its behavior according to the local nature of the nonlinearities, acting more like a GSF when Gaussian approximations are reliable and more like a PF when they are not. In a target-tracking application, we demonstrate that AGSF is efficient and robust to common failure modes of both GSFs and PFs. We empirically validate the switching behavior of the adaptive mechanism in a toy example.

翻译：状态空间模型（SSM）是一类描述动态系统的广泛概率模型，在工程与科学领域具有众多应用。贝叶斯滤波仅在线性高斯设定下具有解析解，此时卡尔曼滤波器可得到精确后验分布。对于非线性或非高斯SSM，则需要近似方法。两类主要的近似方法家族是高斯和滤波器（GSF）与粒子滤波器（PF）。前者依赖局部高斯逼近与数值积分方案，后者采用序贯蒙特卡洛采样。尽管取得了成功，但GSF在强非线性场景下可能遭遇数值不稳定和严重失效问题，而PF虽灵活稳健但往往需要大量计算资源才能获得准确估计。本文提出增强型高斯和滤波器（AGSF）——一种通过隐变量与可调协方差参数参数化的增强高斯近似，从而融合GSF与PF的新型滤波框架。通过调整协方差，AGSF可在GSF-like与PF-like行为间连续插值，将两者作为特例复现。基于此视角，我们进一步开发了自适应AGSF，其可根据非线性性质的局部特征自动调整行为：当高斯近似可靠时更接近GSF，反之则更接近PF。在目标跟踪应用中，我们证明AGSF既能有效应对GSF与PF的常见失效模式，又保持计算高效性。最后通过玩具示例实验验证了自适应机制的切换行为。