Google does track your mobile location history if you use Google Maps to navigate to places.
If you use Google Maps to navigate from place to place, or if you have agreed to be a local guide for Google Maps, there is a chance that you have seen Google Mobile Location history information. There is a Google Account Help page about how to Manage or delete your Location History. The mobile location history page starts off by telling us:
Your Location History helps you get better results and recommendations on Google products. For example, you can see recommendations based on places you’ve visited with signed-in devices or traffic predictions for your daily commute.
You may see this history as your timeline, and there is a Google Help page to View or edit your timeline. This page starts out by telling us: