This paper proposes a theoretical framework for estimating a target-object shape, the location of which is not given, by using mobile distance sensors the locations of which are also unknown. Typically, mobile sensors are mounted on vehicles. Each sensor continuously measures the distance from it to the target object. The proposed framework does not require any positioning function, anchor-location information, or additional mechanisms to obtain side information such as angle of arrival of signal. Under the assumption of a convex polygon target object, each edge length and vertex angle and their combinations are estimated and finally the shape of the target object is estimated. To the best of our knowledge, this is the first result in which a target-object shape was estimated by using the data of distance sensors without using their locations.