Comment by mnw21cam

In this case, a precision transit instrument can be the two corners of two houses (or some other structure that won't move) that are separated by a reasonable distance, an eyeball, and an accurate time. Stand at one and sight along both edges looking South past the other wall, and mark the exact time when a star disappears behind the far wall. That'll give you a load of pretty accurate relative right ascension values. If you can measure the time the the star disappears to within about a second, that gives you an accuracy of 15 arcseconds. If you use a video camera and frame-count, you can get better than that. It'll be best if the far wall is accurately straight and vertical and accurately due South from your observation position. You can get declination values by marking how high on the far wall the star was when it disappeared, or indeed the position in the video when it disappeared, and that accuracy will be the zoom level of your camera. (Make sure you calibrate out the distortions of the camera lens. Creating a panorama in daytime and processing it in something like hugin will give you this.)