What is principle of inverse modeling?
To my understanding, the question refers to studies which aim to estimate pollutant emission fluxes using satellite retrievals of atmospheric constituents. Mathematically, this means estimating the forcing term in an advection-diffusion-reaction system given a set of tracer observations. 

How well you can localize the emissions depends on the pollutant: for something shortlived, like NO2, a given observation will be influenced by a relatively small area, while for a long-lived pollutant (say CO) the effective resolution would be much lower. For long-lived pollutants, the problem is not well posed and needs to be regularized in some way. Typically, instead of reconstructing the emission from a scratch, you try to just refine an existing emission inventory. 

The issues you mention regarding model errors are real and certainly do introduce biases in any emission estimates based on satellite products. This is quite well understood by people working on the field, but the difficulty is in quantifying the errors that are due to model uncertainty.


  How to generate a relative precise relationship between satellite data
  and source emission in consideration of these doubts?


Opinions vary. In my experience, few scientists believe that satellite-based emissions could replace traditional emission inventories. On the other hand, for many areas and pollutants, the regular emission inventories also involve a lot of extrapolation. Ultimately, the question is whether the inverse modeling can deliver some useful added value compared to the existing inventories.