An antenna array system comprises a plurality of antenna elements arranged in an antenna array in a geometric shape. The antenna array system further includes a first sub-array that forms an interior of the antenna array and a second sub-array that forms an exterior of the antenna array. In addition, the first sub-array is a subset of the second sub-array. A number of antenna elements in the first sub-array is greater than a number of antenna elements in the second sub-array. The antenna array system determines an exact satellite location of a satellite within a solid angle of ambiguity using a first virtual pattern and a second virtual pattern.