There is no fixed point :)

But you have your 'local point' of reference to define others motion from. Einstein split motion in two definitions, (relative) uniform motion, versus, accelerations (in GR uniform accelerations being equivalent to 'gravity')

Uniform (relative) motion is the same for all, no matter what 'speed/velocity' you locally might define for some other object. And that one has been tested to be true. That's also one reason why it's called 'relative motion'.

Accelerations we all know that we can discern directly in our bodies, so that type is definable as something unique to the body accelerating. And that's it, uniform motions is what the universe prefer, it spends no, or at least very little, 'energy' to maintain a uniform (relative you) defined 'motion'. So you should then become your own 'fixed uniformly moving point' from where all other motions are defined, assuming you to move uniformly now.

=

And this must be true viewing 'motion' from the Higgs model too btw, all uniform motions being equivalent, as I see it.