Comparing my circumstances to Tycho's:
My advantages:
Scientifically advanced culture, although the new right-wing Dark Ages may be hovering nearby
Astrology in disrepute
Better technology
accurate clocks
telescopes and satellites
personal computers
modern star catalogs
imaging detectors
My disadvantages:
poor funding - a few kilo$ maximum ( 1% of my country's GDP would be about $200B - easily adequate for the task)
no assistants - but computer capability compensates
short timespan - a couple of years investment, not enough to see precession easily or to wait for favorable geometries
I decided to execute the following project to emulate, in some way, Tycho's project to create a star catalog with a few arc minute accuracy
Build my own instrument and observatory, capable of making measurements similar to Tycho's
Use that instrument to capture a dataset parallel to Tycho's
Reduce that dataset to create a star catalog similar to Tycho's
I specifically have:
Not used modern clocks for the catalog - good clocks make the determination of a star's right ascension trivial
Not recreated Tycho's instruments (this is not a re-enactment exercise)
Not automated the entire process. Each measurement will be made by hand-guidance of my instrument
I specifically have:
Used optical aid - 1.5 inch aperture - I can, by eye, see third magnitude stars rarely from my site - most of Tycho's stars not visible
Used an imaging detector - to gain sufficient sensitivity to see all his stars
Used computers instead of assistants. I need to use 'goto' type pointing because most of his stars are not visible to me.
Used modern catalogs to aid in pointing, to verify performance, and to reduce zero-point errors