高斯滤波器的新视角与扩展
A New Perspective and Extension of the Gaussian Filter
摘要：
高斯滤波器（GF）是最广泛使用的滤波算法之一;实例是扩展卡尔曼滤波器、无迹卡尔曼滤波器和差分滤波器。GF通过高斯表示当前状态的置信度，其中平均值是测量的仿射函数。我们表明，这种表示可能是过于严格的非线性观测模型，以准确地捕捉系统中的依赖关系，我们研究如何GF可以推广，以减轻这个问题。为此，我们从变分推理的角度来看GF。我们分析了如何在保持简单性和效率的同时放松对信仰形式的限制。这种分析为GF的推广提供了基础。我们提出了一个这样的推广，这符合使用虚拟测量的GF，通过应用非线性函数的实际测量。数值实验表明，所提出的特征高斯滤波器（FGF）可以有一个显着的性能优势，比标准的GF系统的非线性观测模型。
英文摘要：
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF from a variational-inference perspective. We analyse how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.
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。
