A canonical industrial filtering situation is considered whereby state estimates are required for feedback control purposes and parameter estimates are required because of an unknown and varying output disturbance. It is shown that the order of the extended Kalman filter may be reduced considerably by careful modelling. The disturbance is modelled using a modification to a technique proposed by Panuska. This modification allows parameters which can be assumed known tobe removed from the state equations. This latter method may also be applied to simplifying the identification algorithms used in self-tuning systems.