I've found that there may possibly be many meanings of "objectively analyzed" and "objective analysis" in modeling and data assimilation. What are some of the accepted meanings?
The same method is also referred to as objective mapping or Gauss-Markov smoothing. In this case OA is a least squared interpolation where the estimate is unbiased and the expected error is a minimum in the least squares sense.
In many other cases, objective analysis is taken to be a specific type of optimal interpolation. A good example is the group from University of Liege. In this case OI includes other methods like kriging, successive corrections or the Cressman method.
In my case, I tend to follow the nomenclature and suggestions by Ide et al. (1997).