GNSS antenna system for receiving GNSS signals, in particular GPS, GLONASS, BDS or Galileo, comprising • at least one inverted F-antenna configured to receive GNSS signals in the L1 frequency band (L1-antenna), and • at least one inverted F-antenna configured to receive GNSS signals in the L2/L5 frequency band (L2/L5-antenna), wherein each inverted F-antenna comprises an antenna (2,3) having an antenna end point and a grounded end, a ground plane and a feed, wherein the feed is connected at an intermediate point to the antenna (2,3) and wherein the antenna (2,3) is connected at the grounded end to the ground plane, each inverted F-antenna having a direction defined between the grounded end and the antenna end point, wherein the GNSS antenna system comprises four L1-antennas and four L2/L5-antennas, wherein • a first L1-antenna of the four L1-antennas is oriented in a first direction, • a second L1-antenna of the four L1-antennas is oriented in a second direction substantially orthogonal to the first direction, • a third L1-antenna of the four L1-antennas is oriented in a third direction substantially orthogonal to the second direction and substantially antiparallel to the first direction, and • a fourth antenna of the four L1-antennas is oriented in a fourth direction substantially orthogonal to the third direction and substantially antiparallel to the second direction, wherein each L2/L5-antenna of the four L2/L5-antennas has a corresponding L1-antenna and wherein the direction of each L2/L5-antenna substantially corresponds to the direction of the corresponding L1-antenna, characterized in that each antenna of the four L1-antennas has an average distance to its respective ground plane, the average distance being the distance between the intermediate point and the ground plane or being an actual average in distance between antenna and ground plane along the antenna, and the average distance of at least one of the four L1-antennas differs from the average distance of the remaining L1-antennas. • at least one inverted F-antenna configured to receive GNSS signals in the L1 frequency band (L1-antenna), and • at least one inverted F-antenna configured to receive GNSS signals in the L2/L5 frequency band (L2/L5-antenna), wherein each inverted F-antenna comprises an antenna (2,3) having an antenna end point and a grounded end, a ground plane and a feed, wherein the feed is connected at an intermediate point to the antenna (2,3) and wherein the antenna (2,3) is connected at the grounded end to the ground plane, each inverted F-antenna having a direction defined between the grounded end and the antenna end point, wherein the GNSS antenna system comprises four L1-antennas and four L2/L5-antennas, wherein • a first L1-antenna of the four L1-antennas is oriented in a first direction, • a second L1-antenna of the four L1-antennas is oriented in a second direction substantially orthogonal to the first direction, • a third L1-antenna of the four L1-antennas is oriented in a third direction substantially orthogonal to the second direction and substantially antiparallel to the first direction, and • a fourth antenna of the four L1-antennas is oriented in a fourth direction substantially orthogonal to the third direction and substantially antiparallel to the second direction, • a first L1-antenna of the four L1-antennas is oriented in a first direction, • a second L1-antenna of the four L1-antennas is oriented in a second direction substantially orthogonal to the first direction, • a third L1-antenna of the four L1-antennas is oriented in a third direction substantially orthogonal to the second direction and substantially antiparallel to the first direction, and • a fourth antenna of the four L1-antennas is oriented in a fourth direction substantially orthogonal to the third direction and substantially antiparallel to the second direction, wherein each L2/L5-antenna of the four L2/L5-antennas has a corresponding L1-antenna and wherein the direction of each L2/L5-antenna substantially corresponds to the direction of the corresponding L1-antenna, characterized in that each antenna of the four L1-antennas has an average distance to its respective ground plane, the average distance being the distance between the intermediate point and the ground plane or being an actual average in distance between antenna and ground plane along the antenna, and the average distance of at least one of the four L1-antennas differs from the average distance of the remaining L1-antennas.