We present a collection of variance models for estimators obtained by geometric systematic sampling with test points, quadrats, and n-boxes in general, on a bounded domain in n-dimensional Euclidean space R(n), n = 1, 2, ... , and for systematic rays and sectors on the circle. The approach adopted - termed the filtering approach - is new and different from the current transitive approach. This report is only preliminary, however, because it includes only variance models in terms of the covariogram of the measurement function. The estimation step is in preparation.