AI 中文总结
本文针对非线性多模态状态估计问题，提出自适应拆分-合并高斯混合滤波器（AMF），通过拆分合并高斯粒子实现高效准确的PDF估计，在多基准测试中性能优于基线滤波器，还提出了其并行实现方案。
AI 中文摘要
滤波算法将模型预测与测量值相结合，以估计系统状态随时间变化的概率密度函数（PDF）。在具有振荡或混沌动力学的非线性系统中，PDF常呈现高度不对称甚至多模态的特征，这类非高斯特性违背了卡尔曼类滤波器所基于的单高斯假设。为解决该问题，高斯混合滤波被提出，但准确传播混合成分并随时间自适应调整其数量与权重仍是未解决的挑战。本文提出自适应拆分-合并高斯混合滤波器（AMF），通过自适应拆分与合并高斯粒子（无需辅助在线数值优化）来估计不对称与多模态PDF的时间演化。值得注意的是，所提出的拆分方法可保证沿高斯粒子的目标水平集点方向的方差降低，这使粒子的传播既准确又高效。我们在各类基准测试中表明，AMF的性能始终优于多种基线滤波器，包括单耦合快慢范德波尔振荡器及洛伦兹吸引子；我们还提出了AMF的并行实现，可在实际计算成本下实现高保真PDF估计。
英文摘要
Filtering combines model predictions with measurements to estimate the probability density function (PDF) of a system state over time. The PDF often becomes highly asymmetric and even multimodal in nonlinear systems with oscillatory or chaotic dynamics. Such non-Gaussian features violate the single-Gaussian assumption underlying Kalman-type filters. To address this problem, Gaussian mixture filtering has been proposed. However, accurately propagating mixture components and adaptively adjusting their number and weights over time remain open challenges. Here, we develop an adaptive split-combine Gaussian mixture filter (AMF) that estimates the time evolution of asymmetric and multimodal PDFs by adaptively splitting and combining Gaussian particles without auxiliary online numerical optimization. Notably, the proposed splitting method guarantees a reduction in variance along a target level-set-point direction of a Gaussian particle. This enables accurate and efficient propagation of particles. We show that AMF consistently outperforms various baseline filters across diverse benchmarks, including single and coupled slow-fast Van der Pol oscillators and the Lorenz attractor. We also propose a parallel implementation of AMF, allowing high-fidelity PDF estimation with practical computational cost.
Comments60 pages, 13 figures
