Supply astrometry (either upload a file or cut-and-paste into a text box), and Find_Orb will compute an orbit, residuals, and ephemerides. Note that the on-line version is a stripped-down version of this software.
Supply astrometry (either upload a file or cut-and-paste into a text box), and Sat_ID will list satellites in that area with similar motion. This won't identify every artificial satellite; new ones are occasionally found. But it's usually pretty good.
Lists all objects currently on the NEOCP, giving magnitudes, current uncertainty in the ephemeris position and what it'll be a day from now, MOIDs, etc. The idea is to help in figuring out which objects really ought to be followed up, which can be followed up later, and which ones are "lost".
For a given date/time and MPC code, this will give you accurate positions for all visible GPS satellites. Really verifying that the time reported with your astrometry is actually the time the object was observed is extremely difficult; it's not enough just to sync your computer to NTP or GPS. Timing errors are rampant in astrometry. GPS satellites have well-determined ephemerides and move fast, making timing errors very obvious and easy to measure.
MPC maintains a list of the most recent MPECs. My index covers all of them, and gives you a little summary of orbital parameters for each object.
C/C++ source code for most of these projects, and a variety of other astronomy-related software.
Supply astrometry (either upload a file or cut-and-paste into a text box), and AstCheck will list asteroids in that area moving with that motion. This is roughly similar to MPC's MPChecker (Minor Planet Checker), but it's somewhat faster and takes the object's motion into account, not just its position. That allows it to make identifications with some confidence even if the object is off prediction.
Here, you don't have to supply astrometry. Just enter the object name for anything on the NEOCP, and it'll compute an ephemeris for your location.