Estimation of state and measurement noise characteristics

The paper deals with the estimation of the noise characteristics of a linear system described by the state space model. In particular, the stress is laid on the linear systems with the measurement noise correlated in time. The method, providing unbiased estimates of the state and measurement noise characteristics is analytically derived. The method extends, in principle, the concept of the correlation methods by explicit consideration of the noise time-correlation. The method is also modified into the form suitable for a sensor calibration procedure typically realized by the Allan variance method. The theoretical results are thoroughly discussed and the proposed method is validated using numerical examples.