A Modeling and Filtering Framework for Linear Implicit Systems
Thomas B. Schön, Markus Gerdin, Torkel Glad, Fredrik Gustafsson · 2003
General approaches to modeling, for instance using object-oriented software, lead to di#erential algebraic equations (DAE), also called implicit systems. 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.