This paper considers the problem of reduction of self-localization errors in multi-agent autonomous formations when only distance measurements are available to the agents in a globally rigid formation. It is shown that there is a relationship between different selections of anchors, agents with exactly known positions, and the error induced by measurement error on localization solution. This fact is exploited to develop a mechanism to select anchors in order to minimize the effects of inter-agent distance measurement errors on localization solution. Finally, some simulation results are presented to demonstrate the optimal anchor selection for a particular general class of formations, the globally rigid formations. (c) 2009 Elsevier Ltd. All rights reserved.