A lot of applications of sensor networks require the position of human and objects in indoor environment. There are some methods for this purpose. In this paper, we use received signal strength (RSS) to estimate the position. However, RSS varies substantially owing to fading, shadowing and multipath effects. Attenuation constant varies according to indoor environment. For this reason, the attenuation constant is determined before estimating the position of target node in the conventional method. We propose a position estimation method that estimates a target node position and attenuation constant simultaneously. Thus, the proposed method has no need to estimate the attenuation constant in the target environment preliminarily. To evaluate the position estimation accuracy of the proposed method, we developed the prototype system and experimented in our office. Multiple fixed target nodes were set in the target environment. The experiment presents that the proposed method has about the same accuracy as the conventional one without preliminary data collection for attenuation constant estimation.