> if a bunch of people installed fixed GPS sensors at home

Similar things already exist - although it's used for increasing GPS precision and detecting faulty satellites, moreso than detecting jamming, so the networks might not be dense enough to detect small areas of jamming.

For one state's example, see [1] - choose 'RINEX archives' if you want historical readings.

[1] http://www.wsrn.org/Map/SensorMap.aspx