This paper describes a filtering algorithm for measurements from dynamical systems which are corrupted by noise. The standard Kalman filter is applicable only to systems which can be modelled by linear ordinary differential equations. In this work, the basic idea of the Kalman filter is extended to the more general case of systems which require a differential algebraic (DAE) system as the numerical model. The paper describes the mathematical formulation of this extension to the Kalman filter and its implementation. Finally some results obtained with a test system are given.