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Gravitational field maps are used to correct navigational errors that tend to accumulate in some navigational systems presently in use on unmanned underwater vehicles (UUVs). Two essential elements of such a system are an algorithm to calculate field maps from sparsely and irregularly sampled measured field data and an algorithm to match locally measured field values to an a priori field map. A kriging algorithm is used to calculate a variety of field maps from both simulated and measured field data that vary in resolution and in the density of data used to calculate the maps. Then, navigational errors are simulated and a novel map-matching algorithm is used with the various field maps to assess both the utility of the map-matching algorithm and the effect of map resolution and the density of measured data on the accuracy of the navigational solution. It is shown that although the accuracy of the navigational solution depends on the resolution of the field map, the number of local field samples along the UUV path, the location of the UUV path on the field map and the initial navigation errors, that a kriging algorithm may be used with sparse arrays of measured gravitational-field data.