Experiment planning and identification in a quasilinear regression problem (Q1063569)

The following linear measurement model \(Y_ n=h_ n^ T\theta +\xi_ n\) is considered where \(\theta\) is a vector of unknown and estimable parameters, \(h_ n\) is a vector that defines the program of the \(n\)-th measurement and \(\{\xi_ n\}\) is a noncorrelated sequence. This work solves the following two problems. A. The identification problem: Find an estimate \({\hat \theta}{}^*_ n\) for an unknown vector \(\theta\) such that for any \({\hat \theta}{}_ n\) the inequality \(J_ n({\hat \theta}^*_ n,\{h^ n_ 1\})\leq J_ n({\hat \theta}_ n,\{h^ n_ 1\})\) is valid, where \(J_ n(\cdot)\) is some criterion and \(\{h^ n_ 1\}\underline{\triangle} \{h_ r,h_ 2,...,h_ n\}.\) B. The experiment planning problem: Find a sequence \(\{h^ n_ 1\}^*\) such that for any other sequence the inequality \(J_ n({\hat \theta}^*_ n,\{h^ n_ 1\}^*)\leq J_ n({\hat \theta}^*_ n,\{h^ n_ 1\})\) is valid.