I don't understand what you are trying to do. What doppler shift are you talking about? What are you planning to "subtract out"? I might be able to answer better if you explained more.
It is simple and straightforward to measure the rotation curves of OTHER GALAXIES. You just focus on a nearby galaxy that is seen flat-edge on. With say the stars on the right side coming at you, and the stars on the left side going away from you. And you can measure the doppler shift of those stars and see how it depends on distance from center.
It's like looking at a transparent turning wheel, edge on. Doppler tells the whole story.
What's hard, I think, is trying to work out the rotation curve for OUR MILKYWAY GALAXY.
You could explain more what you are trying to do, what you want to calculate, and why.
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It sounded from your post that you might want data on our own galaxy, and the solar system's motion in our galaxy. That is more complicated. Different data. Or could you perhaps be talking about the doppler shift in the CMB (microwave background) that is caused by the solar system's motion relative to the universe as a whole?
If you are wondering about the sun's motion around the center of the galaxy, that was determined a long time ago from data on the radial velocities of stars that are nearer the center, and the radial velocities of stars that are farther out from center.
We tend to be overtaking stars that are farther out (and still "ahead" of us) and stars that are nearer in (but "astern" of us) tend to be catching up. So both those classes of stars, statistically on average, are getting closer to us.
I think this method was really not very good, but it was all people could do in the early 20th century. After around 1940 or 1950 there was RADIO ASTRONOMY, looking at the 21 centimeter radiation of huge clouds of hydrogen. They could tell the radial velocity (by doppler) very accurately. Clouds closer to center, and behind us, would be catching up---so they would be getting closer to us. Likewise clouds farther out from center, and ahead, would be getting closer because we were catching up with them. I think the whole thing is a massive game of fitting the model to the data----mostly radial velocity data (rates of something getting closer or getting farther away from us).
I don't have any expert knowledge so let my response here be merely a stopgap. Before long I hope someone with more expertise will come along and help you out.
My guess would be that there is a huge amoung of "raw data" on radial velocities and that it would have been a decades-long and very involved process to derive orbital speeds from that data.
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Better amplify your question some, are you interested in our home galaxy, or in the rotation curves of other galaxies?