Elsevier

Advances in Space Research

Volume 66, Issue 4, 15 August 2020, Pages 810-825
Advances in Space Research

Assessing GPS/Galileo real-time precise point positioning with ambiguity resolution based on phase biases from CNES

https://doi.org/10.1016/j.asr.2020.04.054Get rights and content

Abstract

The real-time precise point positioning (RT PPP) with ambiguity resolution (AR) technique has attracted increasing attention due to its high accuracy and low cost. With the availability of RT precise orbits, clocks, and multi-frequency phase bias products for multi-GNSS constellations, which are provided freely by the Centre National d’Etudes Spatiales (CNES), it is possible now to investigate RT PPP AR based on undifferenced and uncombined PPP model. However, only a few studies described these phase bias model tersely, especially in the multi-frequency and multi-system PPP AR. Moreover, the impact on inter-frequency clock bias (IFCB) for triple-frequency GPS/Galileo RT PPP by using the phase bias products have not been investigated. In this paper, the transformation between multi-frequency phase bias model and integer recovery clock (IRC) model was formulated where IFCBs are well considered. Meanwhile, the convergence time, positioning accuracy, narrow-lane ambiguity N1 fixing rate of GPS/Galileo PPP AR were analyzed by using a modified version of the Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator (PPP-WIZARD). Experiments with GPS/Galileo observation from 50 stations over 32 days were performed in static and kinematic modes. Data were processed with four strategies: dual-frequency float and fixed PPP, triple-frequency float and fixed PPP. Results showed that the effect of the IFCB of GPS Block IIF could be mitigated by using the phase bias products from CNES. Among four solutions, the triple-frequency PPP AR achieved the fastest convergence time of 10.43 and 12.55 min in static and kinematic modes, respectively. The average RMS values are 1.2, 1.5, 3.1 cm in static mode while 2.0, 2.5, 3.8 cm in kinematic mode with the 3 h observation session by triple-frequency PPP AR in the east, north and up directions, respectively. Compared with dual-frequency PPP AR, triple-frequency PPP AR could contribute to improving the performance of convergence time and positioning accuracy, especially when few satellites can be observed.

Introduction

Precise point positioning (PPP) is widely used for scientific research and industrial applications which uses undifferenced pseudorange and carrier phase observations along with precise satellite orbit and clock products (Zumberge et al., 1997, Kouba and Héroux, 2001, Montenbruck et al., 2017). However, a considerable initialization time of traditional dual-frequency float solution PPP, normally more than a few tens of minutes, is required in order to achieve the proper convergence of the ambiguities and other estimate parameters (Li et al., 2019). With the rapid development of the modernization of Global Navigation Satellite Systems (GNSS), the user community will benefit from multi-frequency and multi-system satellites signals due to improved positioning accuracy, reliability and convergence time. In 14 October 2019 the GPS constellation consisted of 31 satellites, including eighteen Block IIR satellites, twelve Block IIF satellites and one Block IIA satellite (https://www.gps.gov/systems/gps/space/#generations). In addition to the existing L1 (1575.42 MHz) and L2 (1227.60 MHz) signals, the main feature of the Block IIF satellites are addition of the third civil signal L5 (1176.45 MHz). As of October 2019, 20 Galileo satellites are in orbit, but two of them are in abnormal state, so 18 Galileo satellites can provide precise positioning service continuously (http://www.esa.int/Our_Activities/Navigation/Galileo). All Galileo satellites can transmit signals on three frequencies, the first frequency E1 (1575.42 MHz) and second frequency E5a (1176.45 MHz) of Galileo is identical to GPS frequency of L1 and L5, respectively, and the third frequency E5b (1207.140 MHz) is close to GPS frequency of L2. The extra frequencies can improve the PPP performance as it has more observations and combinations and is less affected by multipath and ionosphere compared with dual-frequency, but to achieve the high-accuracy positioning solutions and reduce the convergence time, the carrier phase ambiguity should be resolved in the triple-frequency case (Li et al., 2018). The Curtin PPP-RTK (real-time kinematic) platform were designed to support multi-GNSS and multi-frequency and the results based on the Australia networks were analyzed (Odijk et al., 2017). GPS, BDS and Galileo PPP-RTK were analyzed with Curtin PPP-RTK platform from large-scale to small-scale, and the data-sets are collected by various receiver types, the initialization time is reduced to 15 min by applying single-receiver ambiguity resolution (Nadarajah et al., 2018).

Many researchers have demonstrated the carrier phase ambiguity resolution using dual-frequency in recent years (Laurichesse et al., 2009, Ge et al., 2008, Collins et al., 2008), all these methods provide precise products about satellite clocks or uncalibrated phase delay (UPD) by using dual-frequency ionosphere-free combination with reference GNSS networks. Shi and Gao, 2014, Geng et al., 2010 explored the relationship and equivalence between these methods and conducted comprehensive comparison in the system redundancy and the necessary corrections. Ding et al. (2017) established an operational RT system for extracting zenith troposphere delay (ZTD), and the effect of PPP ambiguity resolution was evaluated based on RT satellite orbit/clock products from Centre National d’Etudes Spatiales (CNES). These results revealed that the RT troposphere with an average accuracy of about 8 mm in ZTD can be achieved after an initialization process of approximately 8.5 min by using multi-system observations with ambiguity resolution. Odijk et al. (2015) presented a model which did not need to form extra-wide lane (EWL), wide lane (WL) and narrow (N1), this method is flexibility and advantages in the multi-frequency PPP with ambiguity resolution. Li et al. (2018) proposed the UPD estimation and ambiguity resolution (AR) based on raw PPP model for triple-frequency in BeiDou navigation satellite system (BDS), this method could be extended to the n-frequency (n> = 2) case very easily, and the results showed that convergence time and position accuracy can be significantly improved compared with triple-frequency float solution and dual-frequency AR. (Li et al., 2019, Liu et al., 2019a) developed the method and mathematical model of multi-GNSS integrated PPP AR, and a comprehensive analysis of the ambiguity resolved PPP with multi-GNSS was made. Results shown that the multi-GNSS combined ambiguity-fixed system has the fastest convergence speed and the highest accuracy, compared with single system. Geng and Guo (2020) have developed an extendable GNSS PPP model to exploit the advanced Galileo/BeiDou-3 more-than three-frequency signals with single-epoch 10–30 cm positioning accuracy and over 99% availability for the horizontal components over wide areas. Pan et al. (2017) analyzed the characteristics of inter-frequency clock bias (IFCB) and proposed a triple-frequency PPP model that takes the IFCB into account. Their results shown that the triple-frequency PPP improved the positioning accuracy by 19, 13 and 21% in the east, north and up coordinate components by using 3-h datasets, respectively, when compared with L1-/L2-based PPP.

In order to provide a suitable representation for multi-frequency AR, Laurichesse and Blot (2016) presented new uncombined phase bias model. This model is compatible with Radio Technical Commission for Maritime Services (RTCM), and can be extended to the triple- or even more frequency case very easily. Using this uncombined phase bias products with code satellite clocks (International GNSS Service convention), it allows that different AR methods are implemented between the network and user side, and users can employ the AR method of their own choice (Laurichesse and Blot, 2016). The uncombined phase bias products are broadcasted in real-time with an updating rate of 5 s on the mountpoint CLK93 from the CNES caster (ntrip.gnsslab.cn: 2101), these real-time products are also saved as files and available from the web site (http://www.ppp-wizard.net/products/). As of October 2019, EWL, WL, and N1 ambiguity in GPS and Galileo can be fixed in the user side, but integer property of EWL an WL ambiguity can only be recovered in GLONASS and BDS system (this information can be obtained from the signal integer indicator of real-time phase bias messages). Using real measurements with uncombined phase bias products, Laurichesse and Banville (2018) shown that the integer ambiguity of phase measurement can be fixed in the user side. However, only a few studies described this new uncombined phase bias model tersely (Laurichesse and Blot, 2016, Laurichesse and Banville, 2018, Junior, 2018, Duong et al., 2019), especially in the multi-frequency and multi-system PPP AR, and the impact on IFCB for GPS/Galileo RT PPP by using the code and phase bias products have not been investigated. Therefore, we think that there is still of necessity to carry out detailed researches on these topics, so as to better understand the phase bias model, and assess the performance of GPS/Galileo RT PPP AR.

This study aims at formulating the new uncombined phase bias model which is proposed by Laurichesse and Blot (2016) for multi-frequency PPP AR in detail. Then, the performance of phase bias products is assessed in multi-frequency static and kinematic GPS/Galileo PPP AR. In this paper, a modified version of the Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator (PPP-WIZARD) was used (Laurichesse and Privat, 2015), which is provided by CNES under the PPP-WIZARD project. The rest of the paper is organized as follow: Section 2 presents the triple-frequency undifferenced and uncombined GPS/Galileo observation model with code satellite clocks, and explains the reason why resolving the undifferenced integer ambiguity of this triple-frequency model is not feasible. Section 3 introduces the transformation between uncombined phase bias model and integer recovery clock model (IRC model) in the dual- and triple-frequency case. Section 4 describes the PPP AR processing strategy and experiment scenario, analyses the impact of phase bias products on IFCB in the triple-frequency GPS/Galileo PPP, and assesses the performance of uncombined phase bias products in terms of positioning accuracy, convergence time, N1 ambiguity fixed rate and residuals distributions of WL and N1 ambiguity. Finally, Section 5 presents the conclusions and perspectives.

Section snippets

Triple-frequency undifferenced and uncombined observation model

For a specific GPS/Galileo satellite s and receiver r, the raw observations of code P and carrier-phase L at frequency fi can be written as:Pr,isys,s=Dr,isys,s+cdtrsys-dtIGSsys,s+γisys·I1sys,s+ms·zwdr+br,Pisys-bPisys,s+er,isλisysLr,isys,s=Dr,isys,s+cdtrsys-dtIGSsys,s-γisys·I1sys,s+ms·zwdr+λisys·Nr,isys,s+br,Lisys-bLisys,s+εr,iswhere sys denotes different satellite system, G for GPS and E for Galileo; i is carrier frequency, i=1,2,5 for GPS and i=1,5a,5b for Galileo; λisys denotes the wavelength

Resolving integer ambiguity based on phase bias products

Resolving integer ambiguity using the integer phase clocks and WL satellite biases is applied to undifferenced GPS phase measurements (Laurichesse et al., 2009), and the performance of PPP AR at the cm level can be achieved in real-time (Laurichesse, 2011). However, Laurichesse and Blot (2016) evoked several drawbacks of this classical undifferenced formulation. Firstly, this formulation makes difficult for a standardization of the bias messages on the RTCM. Secondly, the user side must

Data description and process schemes

In order to validate the effectiveness of phase biases from CNES in dual- and triple-frequency ambiguity resolution based on undifferenced and uncombined PPP model, both static and kinematic experiments are conducted. As shown in Fig. 3, the observation data of 50 MGEX stations for 32-days (1 August 2019 to 1 September 2019) are selected. All these stations can provide L1/L2/L5 for GPS and E1/E5a/E5b for Galileo triple-frequency observables. The station coordinates were estimated every 30 s.

Conclusion

Multi-frequency RT PPP AR with uncombined phase bias products applicable for each single frequency carrier phase measurements are implemented by CNES, which is however not widely adopted by applications yet. In this paper, we have introduced the transformation between phase bias products and IRC model in the dual- and triple-frequency case, and conducted a detailed analysis in the positioning performance of PPP AR based on RT satellite orbit, clock and phase bias products from CNES by using a

Acknowledgments

The authors gratefully acknowledge IGS MGEX for providing GNSS data. We also acknowledge the CNES for providing real-time precise products. This study is supported by The Major Technology Innovation Project of Hubei Province of China (2018AAA066), The National Science Fund for Distinguished Young Scholars (No. 41525014), The Natural Science Innovation Group Foundation of China (No. 41721003), and The National Nature Science Foundation of China (No. 41704030).

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