The Japanese have an alternative to GPS, named Quasi-Zenith Satellite System (QZSS) or 'Michibiki' (みちびき), which currently provides an augmentation to the USA's GPS locally for Japan, but with the addition of a small number of additional satellites can operate independently of GPS.
The satellites have an interesting inclined geosynchronous orbit that means that the ground track is an analemma shape ('figure of eight') over Japan and Australia.
They are interesting in that they do not require on-board atomic clocks. As stated in the Wikipedia article:
QZSS timekeeping and remote synchronization
Although the first generation QZSS timekeeping system (TKS) will be based on the Rb clock, the first QZSS satellites will carry a basic prototype of an experimental crystal clock synchronization system. During the first half of the two year in-orbit test phase, preliminary tests will investigate the feasibility of the atomic clock-less technology which might be employed in the second generation QZSS.
The mentioned QZSS TKS technology is a novel satellite timekeeping system which does not require on-board atomic clocks as used by existing navigation satellite systems such as BeiDou, Galileo, GPS, GLONASS or NavIC system. This concept is differentiated by the employment of a synchronization framework combined with lightweight steerable on-board clocks which act as transponders re-broadcasting the precise time remotely provided by the time synchronization network located on the ground. This allows the system to operate optimally when satellites are in direct contact with the ground station, making it suitable for a system like the Japanese QZSS. Low satellite mass and low satellite manufacturing and launch cost are significant advantages of this system. An outline of this concept as well as two possible implementations of the time synchronization network for QZSS were studied and published in Remote Synchronization Method for the Quasi-Zenith Satellite System and Remote Synchronization Method for the Quasi-Zenith Satellite System: study of a novel satellite timekeeping system which does not require on-board atomic clocks.[non-primary source needed]
The article links to a PhD thesis on the topic which has also been published as a book:
So it seems there are possibilities of viable satellite navigation system approaches other than GPS, which could potentially be bought off-the-shelf from the Japanese.