Helical antennas suitable for practical positioning at mm level have been developed. The antennas possess a cutoff pattern with 20 dB of ground multipath suppression starting from 10 degrees elevation and low total noise figure. They are shaped as a 3 cm-diameter tube, 40 cm high. In open sky conditions, a special version of RTK engine has shown 3 times growth of the contrast ratio versus the common Choke Ring antennas. Dynamic tests have proved that by smoothing out the noise component of the error, the RMS of positioning in vertical coordinate on the 1 mm level is achievable.