Ordinary kriging is a linear estimation system for any intrinsically smooth random field that satisfies the isotropic assumption. In an inherently smooth random field under isotropic assumptions, the mathematical expectation is independent of its location and the covariance is only a function of the distance between points. The covariance function of the random field is usually unknown and needs to be approximated by the variance function, which is also only related to the distance between points. Since the mathematical expectation of the intrinsically smooth random field is equal everywhere, simple kriging itself satisfies the BLUP condition and is easy to solve for its kriging weights.

If the mathematical expectation of the random field is known (usually assumed to be 0), then ordinary kriging degenerates to simple kriging.