A modeling and filtering framework for linear differential-algebraic equations

General approaches to modeling, for instance using object-oriented software, lead to differential-algebraic equations (DAE). As the name reveals, it is a combination of differential and algebraic equations. For state estimation using observed system inputs and outputs in a stochastic framework similar to Kalman filtering, we need to augment the DAE with stochastic disturbances ("process noise"), whose covariance matrix becomes the tuning parameter. We will determine the subspace of possible causal disturbances based on the linear DAE model. This subspace determines all degrees of freedom in the filter design, and a Kalman filter algorithm is given. We illustrate the design on a system with two interconnected rotating masses.