In this paper, we propose a new trajectory estimation method named TRADE (TRAjectory estimation in DEcentralized way). TRADE is a range-free localization algorithm in fully decentralized mobile ad hoc networks. In TRADE, each mobile node periodically transmits messages containing its estimated trajectory information, and re-computes its own trajectory using those from its neighbors. This information exchange considerably contributes to improvement of the position accuracy. Furthermore, we give the optimal design of the protocol based on the analysis of the algorithm property. Through the analysis, we consider how much trajectory information should be exchanged among nodes to estimate the position within a certain error range in the protocol design. We have evaluated the position accuracy under various settings, and have shown the effectiveness of the protocol in the real world through two realistic application examples.