Prior work established a model for uncertain Gauss-Markov (GM) noise that is guaranteed to produce a Kalman filter (KF) covariance matrix that overbounds the estimate error distribution. The derivation was conducted for the continuous-time KF when the GM time constants are only known to reside within specified intervals. This paper first provides a more accessible derivation of the continuous-time result and determines the minimum initial variance of the model. This leads to a new, non-stationary model for uncertain GM noise that we prove yields an overbounding estimate error covariance matrix for both sampled-data and discrete-time systems. The new model is evaluated using covariance analysis for a one-dimensional estimation problem and for an example application in Advanced Receiver Autonomous Integrity Monitoring (ARAIM).

中文翻译：

---

卡尔曼滤波中不确定高斯-马尔可夫噪声的影响

先前的工作为不确定的高斯马尔可夫 (GM) 噪声建立了模型，该模型保证产生超出估计误差分布的卡尔曼滤波器 (KF) 协方差矩阵。当 GM 时间常数仅存在于指定的间隔内时，对连续时间 KF 进行推导。本文首先提供了一个更容易获得的连续时间结果的推导，并确定了模型的最小初始方差。这导致了不确定 GM 噪声的新的非平稳模型，我们证明该模型为采样数据和离散时间系统产生了超界估计误差协方差矩阵。新模型使用协方差分析来评估一维估计问题和高级接收器自主完整性监控 (ARAIM) 中的示例应用。