Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction and measurement and its Gaussian approximation. The bounds can be used to assess the performance of non-linear Gaussian filters and determine those filtering approximations that are most likely to induce error.

翻译：大多数针对非线性系统的卡尔曼滤波器（如无迹卡尔曼滤波器）均基于高斯近似。本文利用庞加莱不等式，对预测值与测量值的真实联合分布与其高斯近似之间的Wasserstein距离进行界定。所得界限可用于评估非线性高斯滤波器的性能，并确定最可能引发误差的滤波近似方法。