Mathematical modelling in cyber-physical construction systems

This paper deals with the problem of mathematical foundation for information block of cyber-physical system (CPS). CPS requires the involvement of a variety of information technologies. Their effectiveness is related to methods of data processing of contaminated data sets. The robust estimation means minimizing asymptotic bias of the estimates in the presence of contaminating observations. In the contrast to the approach of P. Huber and J. Tukey, where robustness is minimizing of the asymptotic variance of estimates, minimax asymptotic bias method is based on the maximum likelihood approach assuming an arbitrary contaminating distribution. Examples of this approach for the most common probability distributions and the ways of applying this approach are also given.