Admissible model noise of variance-constrained filter in a trajectory identification system

With the least-variance characteristic of Kalman filter, the relation between the variance of Kalman filter and intensities of model noise is first analyzed under the condition of a given measurement noise, then an LMI approach-based solution to steady current-estimation-type filter is presented when both intensities of model noise and measurement noise are fixed. For the system with given measurement noise and the restriction of error-variance upper-bound, the filter admits the system to have model noise with intensity as large as possible. An example of the trajectory identification system is proposed to demonstrate the conclusion.