Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering

Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model