Recently, some countries have begun conducting feasibility studies and R&D projects on High Altitude Platform Systems (HAPS). Japan has been investigating the use of an airship system that will function as a stratospheric platform for applications such as environmental monitoring, communications and broadcasting. If pseudolites were mounted on the airships, their GPS-like signals would be stable augmentations that would improve the accuracy, availability, and integrity of GPS-based positioning systems. Also, the sufficient number of HAPS can function as a positioning system independent of GPS. In this paper, a system design of the HAPS-based positioning system and its positioning error analyses are described.