Two fundamentally different approaches of determining normality of the probability density function of the state estimation error are compared by application to a range of test cases. The first method is the Henze-Zirkler test, which operates on a random particle sample. The variability of its result is quantified. Using this method, departure from normality has been found to occur in three stages which are detailed. The second test compares the offset in whitened space of the predicted state to the predicted covariance mean obtained from the unscented transform. This test is much more efficient than the random particle based approach and can be applied using any perturbations model. The comparison is performed on the state estimation error in Cartesian space and using two-body motion without process noise. The more efficient, unscented transform based approach shows excellent agreement with the Henze-Zirkler test for constructed test cases. Application to orbit determination results from passive optical observations assessed with a Batch-Least-Squares orbit determination however reveals some discrepancies which have yet to be understood and underline the importance of rigorous testing.

中文翻译：

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状态不确定性正常检测

通过将其应用于一系列测试案例，比较了确定状态估计误差的概率密度函数的正态性的两种根本不同的方法。第一种方法是Henze-Zirkler检验，该检验对随机粒子样本进行操作。其结果的可变性被量化。使用这种方法，发现偏离正常状态的过程分为三个阶段。第二项测试将预测状态的白色空间中的偏移与从无味变换中获得的预测协方差平均值进行比较。该测试比基于随机粒子的方法有效得多，并且可以使用任何扰动模型来应用。比较是对笛卡尔空间中的状态估计误差并使用没有过程噪声的两体运动进行的。更有效率 基于无味变换的方法在构造的测试用例中与Henze-Zirkler检验显示出极好的一致性。然而，采用批次最小二乘轨道确定法评估的被动光学观测将其应用于轨道确定结果时，发现了一些尚待理解的差异，并强调了严格测试的重要性。