Assessment of GPS + Galileo and multi-frequency Galileo single-epoch precise positioning with network corrections

Jacek Paziewski 0 Pawel Wielgosz 0 0 J. Paziewski (&) P. Wielgosz University of Warmia and Mazury in Olsztyn , Oczapowskiego 2, Olsztyn, Poland Several processing strategies that use dual-frequency GPS-only solution, multi-frequency Galileo-only solution, and finally tightly combined dual-frequency GPS ? Galileo solution were tested and analyzed for their applicability to single-epoch long-range precise positioning. In particular, a multi-system GPS ? Galileo solution was compared to GPS double-frequency solution as well as to Galileo double-, triple-, and quadruple-frequency solutions. Also, the performance of the strategies was analyzed under clear-sky and obstructed satellite visibility in both single-baseline and multi-baseline modes. The results indicate that tightly combined GPS ? Galileo instantaneous positioning has a clear advantage over single-system solutions and provides an accurate and reliable solution. It was also confirmed that application of multi-frequency observations in case of Galileo system has an advantage over a dual-frequency solution. - The key factor in relative positioning is the resolution of double-differenced ambiguities. Generally, for short observing sessions, a reliable ambiguity resolution is more difficult. However, the most challenging task is the correct ambiguity resolution using data from a single epoch in instantaneous positioning (Bock et al. 2000; Odijk 2001; Wielgosz et al. 2005; Genrich and Bock 2006). Recent research concerns the evaluation of rover observations as active nodes of a ground-based augmentation systems (GBAS) network (Zinas et al. 2012), application of new signals from the Galileo system (Odijk et al. 2010, 2012), special conditions between multiple rover receivers (Giorgi et al. 2012), and development and modifications of ambiguity resolution methods (Chang et al. 2005; Cellmer et al. 2010). The modernization of the GPS system will result in an increased number of transmitted signals and frequencies, such as L1, L2, and L5. The Galileo system will offer a number of signals transmitted on frequencies E1, E5a, E5b, E5(E5a ? E5b), and E6. Application of more than two frequencies can be beneficial for ionosphere modeling, which is crucial for the ambiguity resolution. Two overlapping frequencies (1 575.420 MHz for L1/GPS and E1/ Galileo, and 1 176.450 MHz for L5/GPS and E5a/Galileo) will allow creating double-differenced observations between the both systems. This will result in tightly combined processing, taking into account time, coordinate system differences, and receiver inter-system biases (Odijk et al. 2012). It is expected that the introduction of multi-frequency observations from modernized GPS and forthcoming Galileo, as well as application of tightly combined GPS ? Galileo observational model, will lead to an increase in accuracy and reliability of positioning. This will also allow shortening of the observing session and extending the distance between the user receiver and reference network stations (Verhagen 2002; Julien et al. 2004; Odijk et al. 2012). Tiberius et al. (2002) showed on the basis of theoretical studies, that it would be possible to obtain 0.99999999 confidence of the ambiguity resolution with two GNSS constellations. Ji et al. (2007) investigated potential benefits for the ambiguity resolution with new frequency combinations formed on the basis of the new signals from the Galileo system. Zhao et al. (2005) proved that using integrated GPS ? Galileo has an advantage over a single system in terms of accuracy, availability, and reliability. Recent research demonstrated that combined processing of GPS ? GIOVE resulted in advancement in ambiguity resolution success rate (Odijk and Teunissen 2012). We investigate the performance of single-epoch precise positioning with multi-frequency Galileo as well as dualfrequency GPS ? Galileo observations in a tightly combined observational model. Precise single-epoch positioning is particularly vulnerable to the number of received signals and their quality. A reliable ambiguity resolution based on single-epoch data, in comparison with the on-thefly approach, is an extremely difficult and challenging task due to the low number of observations and the lack of change in satellite geometry (Hu et al. 2005, Cellmer et al. 2010; Paziewski et al. 2013). Thus, current positioning algorithms use ionospheric and tropospheric corrections derived from reference networks. Instantaneous solution is resistant to cycle slips or data gaps; it does not require any initialization or re-initialization (Bock et al. 2000), and errors or biases from previous epochs do not influence on the further epochs, i.e., all solutions are independent. The numerical tests presented are based on simulated GNSS observational data (hardware simulator) and in-housedeveloped post-processing softwareGINPOS (GNSS instantaneous positioning software) (Paziewski 2012). Principles of precise positioning relay on double-differenced (DD) carrier phase and pseudo-range observations collected by two receivers. However, double differencing of the observations may be insufficient for error mitigation in baselines with length exceeding *10 km (Rizos 2002). This is due to spatial de-correlation of differential tropospheric, ionospheric, orbital, and clock errors with growing distance between the user and reference stations. An effective method, developed to overcome this issue, is the application of GNSS reference network-derived corrections. Also, in contrast to the single-baseline solution, where accuracy of the solution decreases with the baseline length, a multi-baseline network approach offers solutions almost independent of the distance between the user and the reference station network. Multi-baseline positioning with external ionospheric and geometric corrections can be regarded an extremely effective method of positioning in terms of accuracy, reliability, and session length. GBAS systems that support satellite positioning are based on this concept and are widely used (Hu et al. 2005; Bosy et al. 2007; Kashani et al. 2008). Research studies were conducted on mitigating ionospheric delays in precise positioning. The results indicate that one of the most effective methods is to apply the external ionospheric corrections together with the estimation of residual double-differenced ionospheric delays. This method is often called ionosphere-weighted model (Teunissen 1997; Odijk 2000; Julien et al. 2004; Wielgosz 2010). The overall procedure for positioning methodology as applied here consists of three steps: (1) processing the reference network GNSS data to derive the network corrections, (2) interpolation of ionospheric and tropospheric corrections for the user location, and (3) user solution with application of the network-derived corrections. Below, we present a brief description of the methodology developed to determine the ionospheric and tropospheric corrections from the network using m (...truncated)