General approach to linear optimal estimator of finite number of parameters

A system is considered whose output depends linearly on the pair: finite parameter vector and control. The control and the output belong to some Hilbert spaces. We formulate two problems. The first is in what way one can obtain the parameter vector, under known control and suitable output generated by this control. This problem is called the estimator problem. The second is how to obtain an estimator optimal with respect to disturbed measurements of output and control. We show an application of our results to state observation in dynamic systems.