How do navigators work? (Algorithms)

Question

satellite navigation

Hello!
The essence of the problem is as follows:
I am writing an application on the phone, part of the functionality should be that you need to guide the car along a given route (such as a navigator)! And now I’m interested in what algorithms are used in navigators, namely, I’m interested in how the navigator understands that the car has gone off the “true path” and at what moment does one route point switch to the next?
I can build a route, find out the direction and position of the car, in fact, too! Some crutch ideas come to mind how to use this information to solve the above problems!

Answer 1

OK, but as the device understands, it went off the route! The thought occurred to me that you can use the formula to find a point on a straight line, but somehow it seemed to me a crutch!

Answer 2

the device reports the current coordinates, direction of movement and speed (not always).