Section: Research Program


The behavior of the monitored continuous system is assumed to be described by a parametric model {𝐏θ,θΘ}, where the distribution of the observations (Z0,...,ZN) is characterized by the parameter vector θΘ. An estimating function, for example of the form :

𝒦 N ( θ ) = 1 / N k = 0 N K ( θ , Z k )

is such that 𝐄θ[𝒦N(θ)]=0 for all θΘ. In many situations, 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 (Z0,...,ZN), an estimate of the unknown parameter is then [63]  :

θ ^ N = arg { θ Θ : 𝒦 N ( θ ) = 0 }

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

  • Recursive estimation: the ability to compute θ^N+1 simply from θ^N;

  • Adaptive estimation: the ability to track the true parameter θ* when it is time-varying.