In designing GNSS high-precision positioning antennas it is desirable to achieve Πshaped
pattern which is homogeneous in the top semi-sphere up to the local horizon and has
rapidly decreasing gain in the downwards directions. Such requirements as minimal loss factor
and compactness are reasonably applied. Patch antennas with substrates formed of periodic metal
structures have been developed, the structures substituting common dielectrics. High impedance
surfaces are employed in design of ground planes. Convex and flat ground planes are discussed
and presented; the antenna with a large flat impedance ground plane has allowed to achieve the
level of positioning error below 1mm rms (root mean square) in real time. The antenna serves as
a reference for research purposes. Semitransparent surfaces have been considered as means to
obtain a sharp drop of the gain (cutoff) while crossing a local horizon. Plane and concave
structures have been treated, and potentials for cutoff are also shown. Practical helical travelling
wave and backfire antennas have been realized, with the 1.5mm-rms-positioning error being
achieved. In addition to positioning, the antennas are considered as sensors in atmospheric
research.