What is the most accurate way to call a function every N milliseconds?
On Android you can create Thread with it's own Handler/Message Queue. It's quite accurate. When you see Handler documentation you can see, that it was designed for that.
There are two main uses for a Handler: (1) to schedule messages and runnables to be executed as some point in the future; and (2) to enqueue an action to be performed on a different thread than your own.