On parametric and state estimation: application to a simple academic example

In general the calculations needed to check identifiability have a high complexity. We propose a technique for the parametric estimation and the estimation of the state which consists in computing the derivatives successively of the output function as a linear combination of the states and parameter. The derivative process ends when the number of equations is enough to determine the values of each state and parameter. Finally the observable nonlinear system Σ is carried out into the generalized observability canonical form which admits an observer