Measurement accuracy in Network-RTK

New satellite systems such as the European Galileo and the ongoing modernization of GPS and GLONASS, allow for improvements in accurate positioning. Real Time Kinematic (RTK) is a system that utilises Global Navigation Satellite Systems (GNSS) to provide accurate positioning in real time. In this paper, we describe the error sources in network-RTK, and how the increased number of satellites and new signals are best served to achieve the desired improvement in performance. Using simulations we find that the inclusion of future satellite systems such as Galileo and Compass can reduce the error in the vertical coordinate of the estimated position from 27 mm to 20 mm for a reference network with 70 km between the reference stations. For periods with high spatial variability in the ionosphere, it is important to consider the tradeoff between influence from the ionosphere and from the local environment. A densified network with 35 km between the reference stations results in a similar improvement as the contribution of the new satellite systems. The error in the estimated vertical coordinate is reduced from 27 mm to 18 mm. Using both a densified network and the new satellite systems reduces the error further down to 13 mm. Introduction Real Time Kinematic (RTK) is a system that utilises Global Navigation Satellite Systems (GNSS) to provide accurate positioning in real time. The general idea in RTK is to receive GNSS-signals at a stationary reference with a known position and to use this information to correct measurement data at a roving receiver in another location. The ideal signal is perturbed by ionosphere, troposphere and imperfections related to ephemerides, clocks and multipath (historically also Selective Availability, SA) and thus the calculated position differs from the known. By calculating corrections that mathematically “moves” the reference to its known position and subsequently apply a similar set of corrections to the rover, the rover’s position can also be determined very accurately. As the reference and rover are at different locations, the signals have been perturbed differently and the correction data are therefore affected by uncertainties that compromise the reliability of the rover’s corrected position. The factors that affect the uncertainties can be classified in different ways, e.g. distance dependent, systematic, random, site specific, rapid, frequency dependent (dispersive). With RTK it is also implicit that, in addition to the broadcast code signals that are handled by relatively cheap off-the-shelf products, the carrier phase of the signal is analysed with a geodetic type receiver. With this technique there is a potential for obtaining position coordinates with accuracies of the order of 1 cm. The difference between RTK and network-RTK is that the latter combines data from several reference stations to provide the rover with corrections. With networkRTK the distance dependent errors are interpolated between the reference stations, which allows for increased distance between reference stations without losing position accuracy. More on networkRTK can be found in e.g., Landau et al. [2002], Rizos and Han, [2003], Lim and Rizos [2008]. Background In order to study the different error sources in network-RTK applications, we model the signal received by a single GNSS receiver. The phase observed by a rover (A) and a reference receiver (B) can be described by (1) and (2) respectively, where  is the measured phase in fraction of cycles,  is the signal wavelength,  is the true geometrical distance between the receiver and the satellite, N is the integer number of cycles referred to as the ambiguity parameter and f is the signal frequency. The s t  and r t  represent the satellite and receiver clock errors respectively, o  is the error in the reported satellite orbital model, t  is the signal delay in the lower part of the atmosphere referred to as the troposphere, i  is the signal delay in the ionosphere part of the atmosphere,  is signal multipath, and  is receiver measurement error. A A tA iA oA r A s A A A A t t f N                    ) ( 1 (1) B B tB iB oB r B s B B B B t t f N                    ) ( 1 (2) Forming the difference between the observed signals at the rover and the reference stations, we obtain an observable, denoted with subscript D, that can be used for determining the vector between the rover and reference positions. By multiplying (1) and (2) with the signal wavelength and subtracting them, we obtain a phase difference measurement: D D r D t i o s D D t c t c                      (3) Here, we assume that the local integer ambiguities, N, are resolved. Hence, we can write the displacement range   as: ) ( e t i o r D t D D t c t c                    (4) Where we have now combined the signal multipath,  , and receiver measurement error, into a local effect, e  That is the sought displacement range equals the phase measurement difference including the errors in satellite clocks, local clocks, satellite orbits, delay in the ionosphere, delay in the troposphere, and local effects. Below, we describe the different error sources and explain how they influence the network-RTK position estimates. Modelling Assumptions We assess position estimation errors by mathematically studying the influence of the error sources presented above. We assume a network configuration as outlined in Figure 1. The distance, dref, between the reference stations is 70 km. When positioning a rover as depicted in Figure 1 as a blue circle, we assume the use of information from the surrounding reference stations. In our configuration, the use of measurements from six surrounding reference stations is simulated. Three of those form an inner triangle and the rest form an outer triangle.