A sequence which has properties similar to the innovation sequence is defined. Its properties are used to test whether a particular Kalman filter is performing optimally or not. This test also tells whether the transition matrix Φ and the control matrixG, and/or the noise matricesQandR, are exactly modelled or not. If the filter is not optimal, an identification scheme is developed to estimate those inexact parameters. This scheme is also applicable to determine the steady-state Kalman gain matrix K directly without the immediate determination of the unknownQandR