From AMS Glossary
Commonly known as OI, this procedure provides an estimate of the state of the atmosphere by a weighted least squares fit to observations and a background field, usually provided by a NWP model forecast.
The weights are the inverse of the error covariance matrices for the observations and the background field. The word "optimum" is misleading, because in practice it is difficult to define the error covariances accurately. A more appropriate term is "statistical interpolation."
Daley, R. 1991. Atmospheric Data Analysis. 98–184.