In general, the GPS chip in your device receives signals from satellites to pinpoint its location. The GPS chip doesn’t send any signals back to the satellites. This applies to the chip in your smartphone as well as to the chip in your navigation system. “One” can’t simply open a map to see your location when using any GPS device.
Ok, I assumed that it sends signal in both directions, like wifi or phone. If it cannot, than it seems it is annonymous.
But even if GPS device and smartphone ones are built the same way, the smarphone spreads also telephone signal. In this case everyone who has access to ISP/Internet provider, can now your average location by towers.
The other problem are tracking applications (but let’s skip them for now assuming they are all off) and the system (Android) which scans for nearby wi-fi MACs even on airplane mode.
I’ve also heard that even on Linux installed on smartphone Google can still scan wi-fis (or rather be seen by other wi-fi, not sure here), because it is implemented in the device, not in the operating system.
So, GPS device may be the same on smartphone and it may not send signal back to satellite, but the problem is that smarphone can be tracked e.g. by wi-fi, and GPS alone not.
And even if somehow GPS alone could be tracked, it is much harder to connect it with your true identity.