I/O SNR and Noise Covariances Norm Ratio Relation in Kalman Filter

Kalman filters are used with great success to solve filtering problems in many fields of science and engineering. The ignorance of state noise covariance or the measurement noise covariance often creates difficulties in the practical application of Kalman filters. In this paper, the relation between the Input/Output signal-to-noise ratio (I/O SNR) and the noise covariance norm ratio for the discrete-time steady-state Kalman filter is established. The state or measurement noise covariance can be tuned via the I/O SNR. This result can be applied in time-varying systems and in steady-state systems, without the a priori knowledge of the state or measurement noise covariance.