Data-Driven Identification of Noise Covariances in Kalman Filtering for Virtual Sensing Applications

The optimality of the Kalman filter for state-estimation depends on the knowledge of the process and measurement noise covariance. In applications, these covariances are often treated as tuning parameters, often adjusted in a heuristic manner based on user-defined performance criteria. While several methods to identify them from data exist, some require the use of optimization algorithms, or inversion of large matrices, which is numerically inefficient. In this paper we review a simple data-driven subspace identification approach to estimate the process and measurement noise covariance, and apply it in the context of virtual sensing. The estimates of the noise covariances are obtained from the residuals of a regression of the banks of shifted Kalman filter states obtained from data and the model matrices of the monitored system. The performance of the approach is illustrated on a numerical example of a chain system by comparing the system states in unmeasured locations to the Kalman filter-based predictions.