Optimal conditional estimation: Average case setting (Q5945074)

The author considers an estimation problem appearing in the identification of linear discrete-time systems by reduced complexity methods. In other words we have to find the optimal approximation to an element of a linear normed space (a system) based on noisy information, subject to the restriction that approximations (models) can be selected from a prescribed subspace of the problem element space. The quality of an identification algorithm is measured by its local average performance. For a wide spectrum of norms in the measurement space an optimal algorithm is defined. Expressions for average errors are also given. Algebraic conditions defining the optimal input are set.