A problem frequently encountered in Kalman filtering is the tuning of the noise covariance matrices. Indeed, misspecifying their values can drastically reduce the performance of the Kalman filter. Unfortunately, in most practical cases, noise statistics are not known a priori. This paper focuses on a method relying on subspace model identification theory to determine them accurately. This solution is developed for linear time invariant systems with stationary random disturbances having constant covariance matrices. Practically, these noise covariance matrices are determined from the comparison between an estimated state space representation and the discrete time state space representation involved in the Kalman filter equations. The method developed in this paper departs from most of the solutions available in the literature by the fact that it does not need any tuning parameter to be chosen by the user. After discussing theoretical results, several numerical examples are given to demonstrate the efficiency of the approach.

中文翻译：

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卡尔曼滤波的噪声协方差矩阵估计与子空间模型识别

在卡尔曼滤波中经常遇到的问题是噪声协方差矩阵的调整。确实，错误指定其值可能会大大降低Kalman滤波器的性能。不幸的是，在大多数实际情况下，噪声统计不是先验的。本文重点研究一种依靠子空间模型识别理论来准确确定它们的方法。该解决方案针对具有固定协方差矩阵的平稳随机扰动的线性时不变系统而开发。实际上，这些噪声协方差矩阵是根据卡尔曼滤波器方程所涉及的估计状态空间表示与离散时间状态空间表示之间的比较确定的。本文开发的方法有别于文献中提供的大多数解决方案，因为它不需要用户选择任何调整参数。在讨论了理论结果之后，给出了几个数值示例来证明该方法的有效性。