Calibration is, basically, a method to improve estimation in survey sampling when auxiliary information is available. It is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on the population means (or totals) of a set of auxiliary variables means building weights that when applied to the auxiliaries give exactly their population mean (total).
Implicitly calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary information is available for all units in the population, more complex modelling can be handled by means of model calibration: the auxiliary variables are used to obtain fitted values of the survey variable for all units of the population and estimation weights are sought to satisfy calibration constraints on the fitted values population mean, rather than on the auxiliary variable ones.
Calibration works by modifications of survey weights such that known population characteristics, in practice totals, are reproduced from the sample. For example, in a sample survey of a human population natural auxiliary variables are age and sex. The population structure by age and sex is generally known from the Census and by proper modifications of the survey weights, the population structure may be exactly reproduced by the sample. For variables in the survey correlated with the auxiliary information (Census information for every survey unit) higher precision in estimated totals is obtained by the new weights usually. The favourable situation for calibration is access to Census table for the units in the sample available in the Census registers.
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