A positioning method comprising: providing an initial putative position vector for a shared origin ; determining a position vector (R s ) for the shared origin by solving a geometric algebraic expression that relates: position vectors (r n ) for a plurality of antennas relative to the shared origin, a putative position vector for the shared origin, and phase information measured at each of the plurality of antennas; wherein solving the geometric algebraic expression comprises: determining, via iteration starting with the initial putative position vector, the putative position vector for the shared origin that is parallel to a difference vector defined as the difference between an averaged origin dependent vector and an averaged phase dependent vector, wherein the averaged origin dependent vector is formed from a summation of geometric products, each of which involves two position vectors for a respective antenna and the initial putative position vector for the shared origin, wherein the averaged phase dependent vector is formed from a summation of geometric products involving two position vectors for a respective antenna, and wherein one of the two position vectors is scaled using the phase information for the respective antenna; and positioning an apparatus using the determined position vector for the shared origin. providing an initial putative position vector for a shared origin ; determining a position vector (R s ) for the shared origin by solving a geometric algebraic expression that relates: position vectors (r n ) for a plurality of antennas relative to the shared origin, a putative position vector for the shared origin, and phase information measured at each of the plurality of antennas; position vectors (r n ) for a plurality of antennas relative to the shared origin, a putative position vector for the shared origin, and phase information measured at each of the plurality of antennas; wherein solving the geometric algebraic expression comprises: determining, via iteration starting with the initial putative position vector, the putative position vector for the shared origin that is parallel to a difference vector defined as the difference between an averaged origin dependent vector and an averaged phase dependent vector, wherein the averaged origin dependent vector is formed from a summation of geometric products, each of which involves two position vectors for a respective antenna and the initial putative position vector for the shared origin, wherein the averaged phase dependent vector is formed from a summation of geometric products involving two position vectors for a respective antenna, and wherein one of the two position vectors is scaled using the phase information for the respective antenna; and determining, via iteration starting with the initial putative position vector, the putative position vector for the shared origin that is parallel to a difference vector defined as the difference between an averaged origin dependent vector and an averaged phase dependent vector, wherein the averaged origin dependent vector is formed from a summation of geometric products, each of which involves two position vectors for a respective antenna and the initial putative position vector for the shared origin, wherein the averaged phase dependent vector is formed from a summation of geometric products involving two position vectors for a respective antenna, and wherein one of the two position vectors is scaled using the phase information for the respective antenna; and positioning an apparatus using the determined position vector for the shared origin. <EOS>