基于转移密度近似的高效高斯混合滤波器
Efficient Gaussian Mixture Filters based on Transition Density Approximation
AI总结：
本文提出用轴对齐高斯混合近似真实转移密度，推导出两种方法，使后验密度组件数量恒定，无需显式减少，并在估计质量与计算复杂度间权衡。
摘要：
非线性系统的高斯混合滤波器在计算预测和滤波步骤中的混合物时，通常依赖严重的近似。因此，人们提出了通过高斯混合密度对噪声密度进行离线近似以减少近似误差的方法。这导致组件数量呈指数增长，需要持续进行组件减少，计算复杂度很高。在本文中，核心思想是用轴对齐高斯混合来近似真实转移密度，并推导了两种不同的方法。这些近似自动确保后验密度中的组件数量恒定，无需显式减少。此外，它们允许在估计质量和计算复杂度之间进行权衡。
英文摘要：
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the approximation error have been proposed. This results in exponential growth in the number of components, requiring ongoing component reduction, which is computationally complex. In this paper, the key idea is to approximate the true transition density by an axis-aligned Gaussian mixture, where two different approaches are derived. These approximations automatically ensure a constant number of components in the posterior densities without the need for explicit reduction. In addition, they allow a trade-off between estimation quality and computational complexity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
