We have developed an adhoc wireless positioning network (AWPN) scheme for information-oriented construction that can temporarily and easily provide a positioning area in both indoor and outdoor environments. The particular requirements of AWPNs are easy deployment and easy configuration because the network should be removed on completion of construction and must frequently accompany the active construction section as it shifts from area to area. In this paper, we propose a localization scheme based on the multilateration method to fulfill the requirements of such AWPNs. The proposed scheme locally and dynamically calibrates the attenuation coefficient defined in the path loss model for radio wave propagation in order to reflect local, fresh propagation characteristics. The results of evaluations conducted on the efficacy of our proposed scheme indicate that it reduces the average error by 30% relative to the conventional approach.