Guaranteed robust nonlinear minimax estimation

Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs. It is well known, however, to be extremely sensitive to outliers in the data resulting, e.g., of sensor failures. In this paper, a new method is proposed to robustify minimax estimation by allowing a prespecified number of absolute deviations to become arbitrarily large without modifying the estimates. By combining tools of interval analysis and constraint propagation, it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way, even when the model output is nonlinear in its parameters. The method is illustrated on a problem where the parameters are not globally identifiable, which demonstrates its ability to deal with the case where the minimax solution is not unique.