OnParameterandStateEstimationforLinear Dierential-Algeb raicEquations
Markus Gerdin, Thomas B. Schön, Torkel Glad, Fredrik Gustafsson, Lennart Ljung · 2006
The current demand for more complex models has initiated a shift away from state-space models towards models described by dierential-algeb raic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic dierential-algeb raic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of ecient numerical methods.