Noise covariance estimation via autocovariance least-squares with deadbeat filters

Abstract

Autocovariance least-squares (ALS) is a correlation-based noise covariance estimation method that has received much attention recently. However, most existing works focus on the situation without knowledge of the process and measurement noise shaping matrices, i.e., the latter two are taken to be identity matrices in most existing methods. In practice, one might have some prior structural information about how the process/measurement noises affect the system dynamics/measurements. For the above case where the noise shaping matrices are not identity matrices, concise conditions under which the system noise covariances can be uniquely identified have not been discovered so far. To fill the above gap, in this paper, we propose to use deadbeat filters in the ALS framework. By doing so, we will establish concrete sufficient conditions under which one can uniquely identify the process, measurement, and the cross noise covariance matrices. The above results will also be extended to systems with unknown inputs. Albeit the results might be of limited scope, to the best of our knowledge, this is the first time such conditions have been presented in the literature for standard linear systems and systems with unknown inputs.