I have data of (simulated) measurements of the density content of ionized ozone in the atmosphere with three different satellites. Specifically, I have a unique set of observations x1,x2,x3,...xN for for each satellite S1, S2, S3 (3N total observations) per timestamp. All three satellite observations are time-synchronized and are present roughly in the same lat/lon area during each timestep of the observation. I want to figure out how to 'level' (I hope this is the right term) observations in the same area during the same time.
My problem is clearly stated as follows:
Suppose at timestamp T satellite S1 measures an ionized ozone density of 3 at the latitude and longitude coordinates (L1, L2). S2 and S3 measure an ozone density of 4 and 1 at the latitude and longitude coordinates (L1+k1, L2+k2) and (L1+k3, L2+k4) where k1,k2,k3,k4 are small offsets (~0.2 degrees) of L1 and L2. Suppose I know that S1's measurement is the 'most accurate' (perhaps it is flying directly overhead). How do I estimate two numbers (say e1 and e2) that can be added to 4 and 1 (S2 and S3's measurements) to make these observations more 'in line' with what S1 observes? In fact, modifying S1's observation is also allowed, but in some sense it should be modified the least. Note that we do not really have an idea of the physical processes that cause these ionized ozone densities, so we cannot incorporate any understanding of the physics into this estimation.
I am quite lost and do not know where to start. Any help would be appreciated, and even the simplest of methods are okay!
