Well-posedness of Filtering Problems for Stochastic Linear DAE Models

Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white noise. The result might be that certain physical variables get infinite variance or contain formal differentiations of white noise. The paper gives conditions for well-posedness in terms of certain subspaces defined by the system matrices.