We propose a new error modeling approach for location discovery in sensor networks, in the presence of range measurement noise. Our pair-wise consistency based approach, uses non-parametric statistical techniques to generate a probability density function of the measured distances as an error model, which serves as an objective function in solving the localization problem. The pair-wise consistency approach enables the development of an error model despite a lack of a-priori parametric knowledge of the network. Further, we propose an optimization-based localization algorithm based on this technique in centralized and localized modes of operation. Our algorithm considers the properties of the particular sensor network as well as the properties of the best achievable solution in the network. Moreover, our approach canvasses problems of node deployment to statistically guarantee targeted error measures. Our error models have been evaluated based on CENS datasets using the learn-and-test method. The experimental evaluation of our algorithm indicates that localization of only a few centimeters is consistently achieved when the average and median distance measurement errors are more than a meter, even when the nodes have low connectivity.