Initialization of Physical Parameter Estimates

Grey box models of dynamical systems contain designated parameters with physical interpretation to be estimated from input-output data. This often gives distinct advantages over black-box models in terms of fewer parameters to estimate and hence better statistical accuracy. The basic theory for how this can be done is well established. The main practical obstacle may however be how the search for the estimates should be initialized. In this contribution we review the difficulties and point to a possibility to use Semidefinite Programming via a Sum-Of-Squares formulation to achieve guaranteed consistent initial values for the physical parameters