2. MATHEMATICAL MODELLING OF PPP

PPP techniques have developed into most effective methods of GPS positioning. One of the main drivers for this has been to achieve accurate positioning in large scale application areas without requiring dedicated reference stations. However, traditional PPP also requires longer convergence time to achieve centimetre-level accuracy. Thus, rapid and real time applications of PPP are currently limited. So, in recent years, many mathematical models have been investigated and developed to shorten the convergence time and improve the accuracy in PPP solutions for fixing integer ambiguities (Kouba and Héroux, Reference Kouba and Héroux2001; Bisnath and Gao, Reference Bisnath and Gao2007; Li and Zhang, Reference Li and Zhang2012).

PPP uses undifferenced ionospheric-free both carrier-phase (ɸ) and/or code pseudorange (P) observations collected by dual-frequency receivers for data processing. This technique provides precise positioning by using precise ephemeris and clock products provided by IGS and other organizations.

By applying a set of corrections to these products, PPP performance may be further improved. The other corrections may be classified as: satellite effects (satellite antenna offsets and phase wind-up), site displacement effect (solid earth tides, polar tides, ocean loading, earth rotation parameters) and compatibility considerations (product formats, reference frames, receiver antenna phase centre offsets, modelling/observation conventions) (El-Rabbany, Reference El-Rabbany2006; Weston and Schwieger, Reference Weston and Schwieger2010; Zumberge et al., Reference Zumberge, Heflin, Jefferson, Watkins and Webb1997; Kouba and Héroux, Reference Kouba and Héroux2001; Kouba Reference Kouba2009).

As stated in both Zumbarge et al. (Reference Zumberge, Heflin, Jefferson, Watkins and Webb1997) and Kouba and Heroux (Reference Kouba and Héroux2001), the ionospheric-free combinations of dual-frequency GPS pseudorange (P) and carrier-phase observations (ɸ) depend on the user position, clock, troposphere and ambiguity parameters to reduce the following simplified observation equations:

(1)$$P = \rho + c(dT - dt) + T_r + \varepsilon _p $$

(2)$$ {\it\Phi} = \rho + c(dT - dt) + Tr + N\lambda + \varepsilon {\it\Phi} $$

where

• P is the ionosphere-free combination of P1 and P2 pseudoranges (P3)=(2·546P ₁–1·546P₂)

• ɸ is the ionosphere-free combination of L1 and L2 carrier-phases (L3)=(2·546 λ ₁ɸ ₁–1·546 λ₂ ɸ₂)

• ρ is the geometrical range computed as a function of satellite and station coordinates

• c is the vacuum speed of light

• dT is the station receiver clock offset from the GPS time

• dt is the satellite clock offset from the GPS time

• T _r is the signal path delay due to the neutral-atmosphere (primarily the troposphere)

• N is the non-integer ambiguity of the carrier-phase ionosphere-free combination

• λ ₁, λ₂, λ are the of the carrier-phases L1, L2 and L3-combined (10·7 cm) wavelengths, respectively

• ε _P, ε_ɸ are the relevant measurement noise components, including multipath.

3. KINEMATIC TEST

In order to test the performance of the PPP technique in kinematic application, a field test was conducted in Halic Bay (Golden Horn), Istanbul in August 2009 (Figure 1).

Figure 1.

Location of the Test Study Area, Golden Horn, Istanbul.

In this study, two different types of GPS receivers, i.e., geodetic-grade dual frequency (Ashtech Z-Xtreme) and OEM type single-frequency (Ashtech AC12), were used (Figure 2). The high-end Ashtech Z-Xtreme receiver was chosen because all its performance characteristics are well known.

Figure 2.

Geodetic-grade receiver (left) and OEM receiver (right) used in this study.

The Z-Xtreme receiver is designed to provide surveyors with cost-effective and centimetre-level accuracy positions in a variety of system configurations. The AC12 is a single frequency receiver capable of precise carrier phase output and the carrier phase measurements deliver high accuracy and flexibility for many applications including land and marine navigation, low-cost heading and attitude systems, deformation monitoring, asset and personnel tracking, relative navigation, automotive, military, and even golf course management. Some important features that are offered by the AC12 are:

• • 12-channel continuous tracking with 1 Hz update rate

• • Low power consumption (0·23 watts)

• • User-defined and pre-defined datums

• • Two-way serial port communications

• • L1 frequency

• • Raw data output (code and carrier)

• • Precise carrier-phase tracking (carrier phase measurement accuracy is 3 mm)

• • 1 PPS output accurate to better than 250 nanoseconds

More details about the receiver can be found in the manual (Thales, 2005).

To calculate the true coordinates of the vessel for each epoch using differential techniques, one geodetic-grade GPS receiver was stationed on a reference point with known coordinates on the shore. In the implementation phase of the kinematic test observation, a geodetic-grade GPS receiver (Ashtech Z-Xtreme) and OEM (Ashtech AC12) receiver were connected to a dual frequency GPS antenna via an antenna splitter. This provides collection of GPS data by both receivers under identical conditions. After the static initialization on shore, the GPS antenna was mounted to the vessel and the kinematic test was started (Figure 3). The measurements were performed along several survey profiles and data were collected for approximately 2 hours with a small vessel (Figure 4).

Figure 3.

Kinematic Test in the Study Area.

Figure 4.

Vessel Trajectory.

4. DATA PROCESSING STRATEGY AND PPP ANALYSIS

All collected GPS data were converted to the RINEX format and uploaded to the CSRS-PPP service on the next full day after the data collection day by using the service's interactive web page and choosing kinematic processing mode (Figure 5).

Figure 5.

Online CSRS-PPP Service Web Site (as of June, 2012) (http://www.geod.nrcan.gc.ca/online_data_e.php).

Some time after the submission, an e-mail was received from the service that contained a URL link and estimated PPP-derived coordinates with some additional information. The processing options handled in the estimation of the PPP-derived coordinates are given in Table 1. As can be seen from the table, the service has used code and carrier phase data for the geodetic-grade dual frequency receiver. Also, the service has produced an L1 code-only solution for the OEM type GPS receiver, because the submitted RINEX file contains only single-frequency data. The service used IGS rapid orbit data because the data were sent to the service next day after the collected data (i.e., 1 day latency).

Table 1.

PPP Processing Options for Kinematic Application.

The data collected by geodetic-grade receivers both on the vessel and stationed ashore were processed by the Leica Geosystems commercial GPS processing software, Leica Geo Office (LGO), to obtain reference trajectory. The PPP-derived coordinates from the online service for both geodetic-grade and OEM type receivers were compared with those of relative (differential) technique results epoch by epoch. The differences in position and ellipsoidal heights between the PPP-derived and relative solutions are shown in Figure 6.

Figure 6.

The differences between PPP-derived and relative solutions.

It can be seen from Figure 6 that the positional accuracy reaches 15 cm and for height up to 25 cm for data from the geodetic-grade receiver processed by the PPP technique. At the same time, it can be seen that the results for PPP analyses obtained from the OEM GPS receiver were converged to the results evaluated by relative technique with metres-level accuracies. For the height component, less accurate results were obtained. The basic reason for the lower performance of the OEM receiver is due to the data collection with only the single L1 frequency signal.

5. RESULTS AND DISCUSSION

In this study, the performance of the Precise Point Positioning (PPP) technique in marine applications was investigated using geodetic-grade and OEM GPS receivers through the online Canadian Spatial Reference System (CSRS)-PPP service. After the evaluation of the data obtained from the dual frequency receiver, centimetre to decimetre level position accuracies were achieved. Results obtained from the low-cost single frequency OEM GPS receiver were converged to the relative technique within metre-level accuracy. It was found that the obtained accuracy is good enough for many studies including hydrographical surveys, marine geodesy, navigation and oceanography.

Today, the PPP technique provides high point positioning accuracies by using a single receiver on the absolute positioning principle. Ease of application, low-cost opportunities and precision in point positioning are the main reasons for utilising the system in survey applications. PPP is thus a significant alternative to the classical relative (differential) positioning techniques.

The usability of the CSRS-PPP web-based online service has become popular with the advantages of user-friendly interface, being free-of charge, with no requirement for a license, knowledge of GPS processing software or the complex background to the technique. The user only needs a PC/mobile device with an internet connection and web browser. Moreover, the user may obtain coordinates only a few hours after submitting the collected GPS data to the service. The major drawback of the web service is that the system does not allow users to select the available options above the optimal options set by the system.