The effect of the antenna phase response on the ambiguity resolution

In order to get the best performance from carrier phase -based GNSS positioning methods in terms of accuracy and reliability the factors affecting the signal propagation must be characterized accurately. These carrier phase -based methods include precise point positioning (PPP) as well as real-time kinematic (RTK). While much focus has been put on atmospheric effects, the antenna effects are either ignored (low-end solutions) or handled by utilizing phase center offset and phase center variation (high-end solutions). The latter approach is typical in modern RTK equipment. Survey-grade antennas are designed to have such fine az-imuthal symmetry in the phase response that only elevation- dependent correction must be applied to the observations. This is referred to as the phase center variation. Moreover, the final baseline solution is corrected with the phase center offset in order to map the solution to a physical point in the antenna structure. The approach typically assumes that antennas of the same type have similar spatial response characteristics so that the same correction data can be applied to all the antennas of the same make. However, carrier phase -based techniques have been proposed for consumer-grade devices, in which the antennas are typically cheap, small and unoptimally positioned in the devices. In such cases the phase response may have high asymmetry both in azimuth and elevation and, hence, the current practices may no longer be sufficient. The unmodelled biases, amongst other, have impact on the probability of successful integer ambiguity fixing in RTK. This paper characterizes three antennas designed for GPS LI reception in terms of their magnitude and phase responses as a function of azimuth and elevation of the signal source. Two of the measured antennas were patches mounted in Bluetooth^TMGPS -receivers and one antenna was Trimble Bullet^TMIII that was measured for reference purposes. The phase responses are analyzed in the context of phase center offset and variation. The phase responses are then utilized in estimating the statistics of ambiguity fixing success rates. The measured antennas show varying performance in terms of phase response symmetry. The patches mounted in Bluetooth devices show approximately 70- and 49-degree variation in the phase response depending upon the direction of the signal. The lack of azimuthal symmetry prohibits the use of only elevation- dependent phase center variation tables and suggests the need for a full 3D table. The two antennas also show such differing responses that the use of a single PCV table for the antennas is not feasible. The bullet, however, shows only 4-degree variation and, hence, fine symmetry. Finally, even though the absolute variations in the phase responses are quite significant in antennas mounted in a Bluetooth GPS, the simulations show that these variations do not have a significant effect on the success rates for ambiguity resolution. This is because the probability of having a significant double difference bias turns out to be practically negligible.