We consider the problem of evaluating dynamic consistency in discrete time probabilistic filters that approximate stochastic system state densities with Gaussian mixtures. Dynamic consistency means that the estimated probability distributions correctly describe the actual uncertainties. As such, the problem of consistency testing naturally arises in applications with regards to estimator tuning and validation. However, due to the general complexity of the density functions involved, straightforward approaches for consistency testing of mixture-based estimators have remained challenging to define and implement. This paper derives a new exact result for Gaussian mixture consistency testing within the framework of normalized deviation squared (NDS) statistics. It is shown that NDS test statistics for generic multivariate Gaussian mixture models exactly follow mixtures of generalized chi-square distributions, for which efficient computational tools are available. The accuracy and utility of the resulting consistency tests are numerically demonstrated on static and dynamic mixture estimation examples.

我们考虑在逼近具有混合高斯态的随机系统状态密度的离散时间概率滤波器的动态一致性评估问题。本文推导了在标准化偏差平方（NDS）统计框架内，用于高斯混合一致性测试的新的精确结果，显示出用于一般多变量高斯混合模型的NDS检验统计量确切遵循广义卡方分布的混合分布，进而演示了其在静态和动态混合估计示例中的准确性和实用性。

利用标准化偏差平方统计量对高斯混合滤波器进行精确一致性测试