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Many existing error metrics for estimation performance evaluation can be viewed as measures of central tendency of error (CTE). However, they are not robust because they are sensitive to extreme values or change of “middle” errors. In view of this, we consider estimation performance evaluation with metrics of CTE directly. To design appropriate measures of CTE, two desirable properties named location equivariance and scale equivariance are introduced and some indicators of robustness are presented. A general form called generalized weighted average Euclidean error (GW-AEE) is proposed for designing specific robust error metrics satisfying the two desirable properties. GW-AEE is a general error metric that aggregates several existing error metrics. Iterative mid-range error (IMRE) and several other error metrics based on GW-AEE are proposed for different applications. Compared with the others, IMRE is more efficient and can be applied easily. Robustness analysis of the new error metrics compared with the existing ones is also presented. Robustness and other properties of IMRE are demonstrated by simulation.