Guaranteed robust nonlinear minimax estimation

Abstract

Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between experimental data and corresponding model outputs. However, minimax estimation is well known 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 prespecied 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 identiable, which demonstrates its ability to deal with the case where the minimax solution is not unique.

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