How Quickly/Accurately can iPhone's GPS find/track my new positions while walking?

Imagine I'm walking down the road and let's say that at Time-1 my Fixed Position pinpointed by the GPS is X

After two seconds I change my position and move 1.5 meters further down the road

Can the GPS "catch" that difference and find my next position even if it is just 1.5 meters towards some other direction only 2 seconds after my previous fixed position it had tracked down? And if yes, does it do that in real time or does it take time for it to update that? Will it even "consider" it, track it down as a new position or simply ignore it because of the slight difference (only 1.5 meters further down towards some random direction)

The reason I'm asking is because I'm writing code for an application of mine and basically what I want to do is have the application notify me once I get to X, using GPS

The tricky part is that X is not some shop two blocks down the road. X is just standing 1.5 meters (4.6 feet) away from me towards some direction, the distance is pretty short. And I want the GPS to notify me once I get there.

What's even trickier is that X doesn't even have a distinct fixed position on the planet ( a specific longitude/latitude address that I could just type in my code)

X is just a place that is 1.5 meters (4.6 feet) away from me at a certain angle Y regardless of where I am standing on the planet.

Think of it in terms of a game if you will :

You turn on your app while standing still and now the goal is to find spot X which could be anywhere in a radius of 1.5 meters from where you are standing

The programmer has put in the code that spot X is 143 cm away at a 35,76 degree angle from wherever you are standing when you turn on the app

You start walking around and using GPS the app should let you know when you step on spot X

Remeber that spot X cannot have a specific fixed position (it's not around some corner in some village in northern France for example)

And if I can't do the above using GPS could you think of some other way?