Analytical solution of the steady-state Kalman filter for observing drift on NOx models with application to turbocharged diesel engines

An augmented state-space model for drift correction is proposed adding an extra-state for cancelling drift on a given model or sensor output. A Kalman filter is used for drift observation. The model is Linear Time Invariant and noise covariances are considered constant. Under these assumptions, filter is steady-state and an analytical solution to the Riccati equation can be derived. Current paper gives the analytical solution to the Kalman gain and covariance matrix from using the iterative filter equations.