## Section: Research Program

### Identification

The behavior of the monitored continuous system is assumed to be described by
a parametric model $\{{\mathbf{P}}_{\theta}\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{0.166667em}{0ex}}\theta \in \Theta \}$,
where the distribution of the observations (${Z}_{0},...,{Z}_{N}$)
is characterized by
the parameter vector $\theta \in \Theta $.
An *estimating function*, for example of the form :

is such that ${\mathbf{E}}_{\theta}\left[{\mathcal{K}}_{N}\left(\theta \right)\right]=0$ for all $\theta \in \Theta $. In many situations, $\mathcal{K}$ is the gradient of a function to be minimized : squared prediction error, log-likelihood (up to a sign), .... For performing model identification on the basis of observations $({Z}_{0},...,{Z}_{N})$, an estimate of the unknown parameter is then [63] :

In many applications, such an approach must be improved in the following directions :