A comparison of subspace-based and maximum likelihood noise covariance estimation within Kalman filtering for virtual sensing applications

The process and measurement noise covariances are usually treated as tuning parameters and adjusted in a heuristic manner to fine-tune state estimates of dynamic systems within Kalman filtering. Although there are various strategies to adjust the noise covariance matrices given a dynamic model and available data, many of these methods are not statistically efficient, leading to large state prediction errors. Others require the use of complex optimization algorithms, or involve inversion of large matrices, which is expensive from a computational standpoint. In this work, we study two statistical approaches for noise covariance estimation in stochastic linear time-invariant state-space systems: the first based on a recently published approach based on stochastic subspace identification; the second based on maximization of the likelihood associated with the Kalman filter prediction error, recursively addressed via an Expectation-Maximization algorithm. This study provides a comparison of the achievable performance of both methods within a virtual sensing application, involving estimation of sensor outputs on a 6-DOF chain-like simulation model.