Variance Analysis of Parallel Hammerstein Models

Abstract: In this thesis we generalize some recent results on variance analysis of Hammerstein models. A variance formula for an arbitrary number of parallel blocks is derived. This expression shows that the variance increases in one block due to the estimation of parameters in other blocks but levels off when the number of parameters in other blocks reach the number of parameters in that block. As a second contribution, the problem of how to design the input so that the identification process leads to a more accurate model is considered. In other words, how to choose the input signal so that the model error described previously is minimized, is studied. The investigations show that the optimal input probability density function has a surprisingly simple format. In summary, some of the derived results can be used directly in practice, while some might be used for further research.