In additions to konijn's remarks I would add some other that I would normally add reviewing this code.
Explicit type declarations
In the following code there is no need to declare type:
public debug: boolean = false;
The TypeScritpt compiler will understand the type from the assigned value.
Methods with side effects
You have a method checkForChanges(...
A short review;
Changing CSS for input seems too broad, just apply CSS changes to a class tied to your control
throw new TypeError('Unknown geographic position type.'); seems odd, why throw this if the calling function does not catch it anyway? You need a think on how this control handles exceptions.
Similarly, in degreesToDMS you return null , but the ...