Miyakoda, K., and O. Talagrand, 1971: The assimilation of past data in dynamical analysis. I. Tellus, 23 (4-5), 310-317.

Abstract: A method is presented to reduce the error in meteorological data analysis by using observations taken prior to analysis time, extrapolating them to the present time with the prediction equations, and mixing them with the present observation data. The equations can be non-linear, irreversible, and three-dimensional in space. The time span of the extrapolated data is several days. One-dimensional linear as well as two-dimensional non-linear vorticity equations are treated as examples. The best estimate of the analyzed field is the linear combination of a number of the predicted solutions from the past data with weights included that depend on predictability decay as functions of the data's age.