On the estimation of measurement errors in linear dynamical systems

The article is concerned with the problem of linear dynamical system state estimation subject to noise-corrupted observations. In solution of the linear optimal filtering problem under guaranteed statement the problem of measurement noise identification occurs. The approach to adaptive measurement noise estimation is proposed. It is based on statistical processing of the innovation sequence in the Kalman filter. The special case of linear dynamical system with one-dimensional output the state of which is observed only on a short-time interval is considered and it is shown that statistical characteristics of the innovation sequence can be used for measurement noise identification and also for adjustment of the guaranteed estimates. Simulation results are given to confirm the usefulness of the approach.