State model of pseudoinnovations processes

The structure of the innovations process is examined as the gain of a Kalman filter is allowed to deviate from its optimum structure. The state model of the resulting pseudoinnovations process is determined, and it is shown how the level (or variance) of the process depends on the difference between the desired Kalman gain and the gain actually being employed. The model illustrates requirements on an arbitrary gain matrix to ensure stable filter performance.