Suppose we (a spacecraft, probe, or similar) know our location only to within a few billion km (a few Tm) in any direction in 3D space, and we want to determine our location to a higher degree of precision than this.
That was basically a question on Worldbuilding SE that I answered, where I suggested measuring the angles to known pulsars in order to triangulate one's position in 3D space. The part I didn't know about was exactly how you'd make those angle measurements, so I sort of assumed a naiive approach of basically just looking around using either an optical telescope or a high-gain radio antenna (possibly a phased array that can be reconfigured on the fly, not dissimilar from how modern RF direction finding in 2D is done).
A comment to that answer by Philipp simply states that "You can measure your angle to a pulsar by measuring its red-shift."
How does measuring the redshift help determine the angle to the pulsar, and how would one realistically go about doing it in such a situation?
As far as I understand, redshift can tell us about the relative movement of objects in space that give off EM radiation. But here, we aren't really interested in relative movement, but rather in an angle relative to some known or fixed plane (such as the spacecraft platform). I just don't see how the former realistically helps us establish the latter.
(I'm not a physicist, and don't even play one on TV, so please go easy on me. Some math is fine, though, and I expect might be helpful.)