The realization and convergence analysis of combined PPP based on raw observation

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Abstract

In order to speed up Precise Point Positioning (PPP)’s convergence, a combined PPP method with GPS and GLONASS which is based on using raw observations is proposed, and the positioning results and convergence time have been compared with that of single system. The ionospheric delays and receiver’s Differential Code Bias (DCB) corrections are estimated as unknown parameters in this method. The numerical results show that the combined PPP has not caused significant impacts on the final solutions, but it greatly improved Position Dilution of Precision (PDOP) and convergence speed and enhanced the reliability of the solution. Meanwhile, the convergence speed is greatly influenced by the receiver’s DCB, positioning results in horizontal which are better than 10 cm can be realized within 10 min. In addition, the ionosphere and DCB products can be provided with high precision.

Introduction

Precise Point Positioning (PPP) (Zumberge et al., 1997, Kouba and Héroux, 2001) with accuracies ranging from a few millimeters to a few centimeters. It is widely used in crustal deformation monitoring (Azua et al., 2002, Savage et al., 2004, Hammond and Thatcher, 2005, Calais et al., 2006), real time GNSS meteorology (Gendt et al., 2003, Rocken et al., 2005), orbit determination (Bock et al., 2003, Zhu et al., 2004), time transfer (Roosbeek et al., 2001, Dach et al., 2006), regional seismic activity monitoring (Gordon et al., 2007, Kouba, 2003, Langbein and Bock, 2003). However, the major problem of PPP is that the convergence time is too long. It may take up 30–60 min to obtain the position errors which are smaller than 10 cm while using the traditional ionospheric-free PPP model (Bisnath and Gao, 2007), ambiguity resolution technology (Ge et al., 2008, Geng et al., 2010, Li and Zhang, 2010, Collins and Bisnath, 2011, Collins et al., 2012, Jokinen et al., 2012, Odijk et al., 2012) can shorten the convergence time. However, using only GPS has been discussed in these papers, fixing carrier-phase ambiguities is more difficult in the case of GLONASS PPP. Because GLONASS signals using the Frequency Division Multiple Access, the satellite/frequency/receiver type specific inter-frequency biases in GLONASS code-phase and carrier-phase measurement are difficult to obtain.

Normally, two possible ways will improve PPP’s convergence speed. One way is to add more frequency observations such as the L5 observations (Kubo et al., 2005, Jan, 2002), it is not a perfect way as it lacks of satellites broadcast the L5 observations and will increase the user’s cost for multi-frequency receiver; the other way is to integrate multi-system’s observations (Cai and Gao, 2007, Melgard et al., 2011, Aazb et al., 2011). Fortunately, the GLONASS system is reconstituted. Nowadays, 24 satellites are fully operational, precise orbit and clock products are provided by different organizations (Oleynik et al., 2006, Romero et al., 2004, Weber and Fragner, 2002, Habrich et al., 2004). It provides opportunities to improve PPP’s convergence speed and reliability using the combined observations.

Usually, the combined PPP uses the ionospheric-free model and is processed in observation area whether in real time or post-mission (Cai and Gao, 2007, Jokinen et al., 2011). It has some drawbacks, firstly, it will amplify the observe noise and reduce the numbers of the observation; secondly, the ionosphere and DCB informations will be lost; thirdly, the parameters estimate in observation area is inefficient as the combined PPP has much more equations and parameters.

In this study, the combined PPP is realized based on raw observations with ionospheric delay and receiver’s Differential Code Bias (DCB) estimated as unknown parameters; the ionospheric delay’s estimation are properly constrained by a Global Ionosphere Maps (GIM) and the empirical variation characteristics in temporal and spatial; meanwhile the combination is finished in equation area and usig the parameters pre-eliminate method.

At the beginning of this paper, the combined PPP model which is based on raw observation is introduced, and the error correction strategies are discussed especially for the ionosphere and DCB corrections. Then, the data solution strategy is represent. Afterwards, datasets collected at 40 stations of the International GNSS Service (IGS) from day 074 to 080 in 2012 are used for the validation, the PPP’s solutions and convergence time are compared and analysed between different systems. At the end, some important conclusions are given.

Section snippets

Observation model

The PPP model for a combined GPS and GLONASS system which is based on raw observation can be described as follows:PFi=ρi+cδr-cδi+dtropi+dion/fFi+DCBP,F-DCBP,Fi+εP,FiΦFi=ρi+cδr-cδi+dtropi-dion/fFi+λFNF+εΦ,Fiwhere i is the satellite index. P, Φ are the code and phase measurements. F is the index of frequency. ρi is the geometric distance from satellite to receiver. r, i are the receiver clock error and satellite clock error. dtropi is the tropospheric delay. dion/fFi is the ionospheric delay

Data description

The GPS and GLONASS observation datasets collected at 40 stations of the IGS from day 074 to 080 in 2012, the sampling rate is 30 s. Fig. 2 showing the distribution of the collected stations, 10 stations which marked with green color are selected for analysing the DCB’s daily variation. In our test, the positioning results provided in three forms: GPS-only results (G), GLONASS-only results (R) and the Combined results (C).

Comparison of satellite numbers and PDOP values

Fig. 3 shows the average numbers of satellites at the selected 40 IGS

Conclusions

The GPS and GLONASS combined PPP which is based on the raw observation has been proposed in this paper. In PPP model, the raw observations are used instead of the ionosphere-free combination, it not only increase the numbers of observations but also reduce the combination noise; in error corrections, the ionosphere errors are estimated with constrains of prior information, temporal and spatial characteristics, the receiver’s DCB is also estimated as an unknown parameter, useful ionosphere and

Acknowledgments

Thanks to the International GNSS Service (IGS) for providing GNSS data. Rui Tu is supported by China Scholarship Council.

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