Global Navigation Satellite Systems (GNSS) are widely used in a variety of geoscience applications [1
], including tectonic plate motion monitoring [2
], surface deformations [3
], landslide monitoring [4
], seismology [5
], as well as ionosphere [6
] and troposphere [7
] remote sensing. A GNSS receiver remains the core sensor in navigation systems of unmanned aerial vehicles [8
] and autonomous vehicles [9
]. Yet the GNSS have revolutionized not only geosciences but also land surveying [10
], as they allow for determining position coordinates with centimeter-level precision in real-time or up to sub-millimeter accuracy in post-processing solutions.
Achieving precise and accurate position coordinates requires a combination of the three following aspects: availability of a well-defined reference frame; processing of carrier-phase measurements, use of an appropriate measurement model. Two general approaches can be distinguished, namely absolute and relative positioning. In absolute positioning, the reference frame for measurements is provided by satellite coordinates, while in relative positioning, a reference station has well-known coordinates. Therefore, the positioning accuracy of a GNSS directly depends on the accuracy of the coordinates of either the satellites or the reference station. The International GNSS Service (IGS, https://www.igs.org/
) provides satellite orbits, clocks, and established control point networks with centimeter-level accuracy, in order to maintain national reference frames all over the world.
The relative positioning is commonly used in land surveying applications, in real-time post-processing. Real-Time Kinematic (RTK) or Network RTK (NRTK) modes allow for achieving centimeter-level accuracy in real-time [11
] if there is a base station or a network of reference stations near the mobile receiver. A millimeter level accuracy can be achieved with a differential approach for long static surveys by means of networks of GNSS receivers separated by tens to hundreds of kilometers [12
]. The dominant technique in absolute positioning is the Precise Point Positioning (PPP) [13
], which works worldwide, even if high-precision results are still limited to static surveys and dual-frequency receivers [14
]. Therefore, the choice of the measurement model should depend on the required positioning accuracy and availability of a local GNSS frame.
Even if both the well-defined reference frame and the chosen measurement model are available, the acquisition of carrier phase measurements remains critical. For many years, such a feature was limited to dual-frequency geodetic-grade receivers, whose high cost was the limiting factor for many applications [15
]. Since low-cost single-frequency receivers capable of logging carrier phase measurements have become available, several studies aimed at investigating their positioning accuracy [17
] and demonstrations of low-cost monitoring applications were performed [19
]. Two main advantages of using low-cost receivers are the possibility of deployment in hazardous areas and logging a higher amount of position data [21
]. Millimeter [15
] to centimeter-level [22
] accuracy can be achieved under favorable conditions [23
], as the antenna is the key factor limiting the positioning accuracy [18
]. Moreover, the ionosphere delay remains a major error source affecting single-frequency PPP [17
] and long-baseline RTK [15
]. Most of the low-cost single-frequency receivers available on the market do not meet their nominal performance in urban areas characterized by the multipath effect [24
After the development of low-cost multi-frequency receivers, the ionosphere delay is no longer an issue and can be removed by combining the measurements obtained at two frequencies. Currently, two dual-frequency receivers are available on the market, namely u-blox ZED-F9P (https://www.u-blox.com
) and SkyTraQ PX1122R (https://www.skytraq.com.tw
). The former is capable of simultaneously tracking four GNSS (GPS, GLONASS, Galileo, and BeiDou). However, the positioning accuracy of low-cost receivers is worse than geodetic-grade receivers, thus increasing the convergence time of a real-time PPP solution [25
]. If a low-cost patch antenna is used, it is needed to correct the carrier phase patterns [26
]. Moreover, these receivers can be used for geodetic surveys in open sky conditions and short baselines [27
Very few studies on the performance of a low-cost receiver combined with a low-cost antenna, used for precise relative and absolute positioning in static and kinematic mode, are available [28
]. Although the manufacturers declare that their receivers enable a reliable positioning in RTK mode with a short convergence time, such a performance is limited to a favorable environment [24
]. Therefore, this paper aims at evaluating the signal acquisition performance and accuracy of a low-cost dual-frequency multi-GNSS receiver, used for a relative (RTK and NRTK) and absolute static positioning in typical land-surveying applications, e.g., establishment of control points and cadastral surveying.
The performance of the low-cost dual-frequency u-blox ZED-F9P receiver, connected to the low-cost ANN-MB-00-00 patch antenna, was evaluated. The current price of the hardware is lower than 250 EUR. C/N0 ratios in such a configuration resulted on average 7 dB Hz lower than those obtained by using geodetic-grade hardware. Still, the low-cost receiver performed well for elevation angles higher than 10°. Low C/N0 ratios for low elevation satellites were attributed to the simplified antenna construction, rather than the receiver itself. The C/N0 differences between GNSS and frequencies were due to varying signal transmission energy. Therefore, multi-GNSS signals acquisition with a low-cost receiver is feasible and has accepted characteristics, but it is worse than that achievable by using a geodetic-grade receiver.
In a static relative positioning under open sky conditions, almost 80% of fixed ambiguities were achieved with a 26 km long baseline. For the 50 km long baseline, the average ambiguity fixing rate did not exceed 60%, as the atmospheric error sources prevented ambiguity fixing. The fixing scores were c.a. 10% to 30% lower than those achievable by using a geodetic-grade receiver with baselines of similar lengths [31
]. Nevertheless, a centimeter-level accuracy could be achieved in the relative positioning. The positioning accuracy increased with the increasing session length but it decreased with the increasing baseline length. For sessions longer than 1 h, a significant improvement was not observed, neither in the ambiguity fixing rate nor in the horizontal and vertical positioning accuracy. Longer sessions are justified for the absolute positioning using the PPP technique, in which the horizontal and vertical accuracy of few centimeters was achieved after 2.5 h of measurements.
In a more challenging surveying environment, i.e., an urban area, an hour-long static relative positioning allowed for achieving a horizontal (2D) and vertical accuracy of 20 and 15 mm, respectively. However, the estimated uncertainties at a 95% confidence level were an order of magnitude smaller. Contrary to baseline solutions, in the absolute positioning, the differences between estimated and known coordinates of control points were much lower than the estimated uncertainties. Differences between the estimated and true coordinates were within the ±10 cm range. Horizontal and vertical RMSE resulted in 62 and 56 mm, respectively. A distinct disagreement between accuracy and uncertainty was justified by stochastic models, which varied in the software and are not optimized for measurements performed by a low-cost receiver. Therefore, a limited confidence in the estimated positioning error, i.e., a posteriori standard deviation, is suggested.
In the RTK mode, a positioning precision exceeding that provided by the manufacturer, i.e., 1 cm + 1 ppm, was achieved. For a baseline shorter than 0.5 km and geodetic-grade base station, the horizontal error reached 33 mm (RMSE was 20 mm) and the vertical component (Up) was overestimated by 52 mm on average, with the highest error of 73 mm (RMSE was 53 mm). The measurements performed by using two low-cost receivers, of which one as a mobile receiver and the other as a base station, led to further degradation of the positioning precision. Still, the positioning accuracy was high, i.e., the RMSE was 60 and 26 mm for the horizontal and vertical components, respectively. In the NRTK mode, the positioning accuracy resulted between the two aforementioned RTK configurations and was in agreement with the horizontal accuracy of 3 cm declared by the NRTK service provider. Last but not least, inaccurate height determination was noticed in RTK surveying by using two low-cost receivers, of which the mobile receiver spins around the base station. A source of this issue was identified in accumulating PCO/PCV errors of the used low-cost antennas, as the highest errors mostly occurred when antennas were in the opposite orientation.
Similar to low-cost single-frequency receivers [25
], low-cost dual-frequency receivers do not meet their nominal performance in urban areas. However, the positioning accuracy achieved in static and RTK/NRTK modes justifies their use in land surveying applications, such as cadastral surveying and mapping, which require sub-decimeter horizontal accuracy. Static positioning using low-cost receivers (both base station and mobile receiver), which achieves baseline accuracy better than 1 cm, is suitable for monitoring applications, including hazard and atmosphere monitoring. Although low-cost solutions, which are tailored for land-surveying, are not available on the market yet, this market is expected to rapidly grow soon.