[michaelt]

Combining GPS with accelerometer and gyroscope is sometimes called "sensor fusion" - one common way of doing it is with a "Kalman filter" and if you google that you'll find a wealth of information.

If you've got plenty of money, companies like https://www.oxts.com/ have working systems available off the shelf. They're used for things like measuring the dynamic performance of cars.

Such systems will sorta work indoors but not very well. The gyroscope/accelerometer will gradually drift; when you're outdoors with a clear view of the sky, the GPS can compensate for that but when you're indoors that isn't possible. How fast the drift happens depends on how much money you spend to get the highest performance gyroscopes and accelerometers.

It's also possible to integrate other sensors, but that's application-dependent; for a car going through a tunnel, an odometer is a great addition, for a smartphone not so much.