The Kepler spacecraft is taking incredibly precise photometric data on tens of thousands of stars for the purpose of detecting exoplanets. For many reasons, the lightcurves it returns are sensitive to the temperature of the spacecraft: The focus and astrometric map (camera calibration) of the camera changes with temperature, and the detector noise properties might be evolving too. This wouldn't be a problem (it's a space mission) but the spacecraft changes its sun angle abruptly to perform high-gain data downlink about once per month, and the temperature recovery profile depends on the orientation of the spacecraft post-downlink. Instead, there are sub-percent-level traces of the temperature history imprinted on every lightcurve. Each lightcurve responds to temperature differently, but each is sensitive.
Of course the spacecraft keeps housekeeping data with temperature information, but it hasn't been extremely useful for calibration purposes. Why not? The onboard temperature sensors are low in signal-to-noise or dynamic range, whereas the lightcurves are good (sometimes) at the part-in-hundred-thousand level. That is, there is far more temperature information in the lightcurves than in the direct temperature data! Here's the project:
Treat the housekeeping data about temperature as providing noisy labels
on the lightcurve data. Find the properties of each lightcurve that best predicts those labels. Combine information from many lightcurves to produce an extremely high signal-to-noise and precise temperature history for the spacecraft. Bonus points for constraining not just the temperature history but a thermal model too.
