We consider measuring Position Mean Squared Error (PMSE) in a time-of-arrival positioning system with sensors of known locations and a fixed node to be located. To measure PMSE without prior knowledge of the true position of the node, it is common practice to assume that an average of all position estimates yields an acceptable estimate of the true position. In the case of biased estimators however, using this assumption no longer holds. In this paper we introduce a novel technique to estimate PMSE for biased estimators which is more robust than the common PMSE estimation approach, in terms of reduced estimation MSE. Our results are validated for the case of biased estimators in the presence of non-line-of-sight errors with both good and poor geometric configurations.