The data for the 4 sites, ALBH, NRC1, STJO and YELL were segmented into 1, 6, 12 and 24 hour data arcs using the software tecq by UNAVCO (2010). The data were submitted to GAPS, returning a solution from APPS, CSRS-PPP and magicGNSS as well. The 3D difference for the four sites were calculated and illustrated in figures 1 to 4 below and tabulated in Table 1. Table 2 contains 3D sigma and 3D difference for 24 hour data arcs from 2000 to 2010.

**Table 1:**

**3D sigma and 3D difference for varying data arcs**

**Table 2:**

**3D sigma and 3D difference for datasets ranging 2000.0014 to 2010.0014**

## Accuracy and precision

To analyze the accuracy and precision of the PPP method, the 24 hour data arcs were examined for the sites ALBH, NRC1, STJO and YELL. In the horizontal components, CSRS-PPP, APPS, GAPS and magicGNSS had a maximum difference in the easting component of 7.5 mm and 1.5 cm in the northing component. In the up component CSRS-PPP, APPS and magicGNSS had a difference of less than 6 mm for all four sites except YELL; CSRS-PPP had a difference 1.3 cm. For GAPS, their solution ranged from 5.4 mm at STJO to 2.3cm at YELL. This indicates that PPP is capable of providing sub-centimeter accuracy in the horizontal component. The accuracy in the up component is site dependant and ranges from sub-centimeter to centimeter depending on efficiently tidal and atmospheric effects are mitigated.

**Figure 2: Easting component for 24 hour data arc Figure 3: Northing component for 24 hour data arc**

**Figure 4: Up component for 24 hour data arc Figure 5: 3D difference 24 hour data arc**

Table 4 below shows the standard deviation of each PPP provider in the northing, easting and up components and 3D amongst the four sites. The standard deviation of the up component was as expected for the PPP providers CSRS-PPP, GAPS and APPS, being approximately three times larger than that of the easting and northing components. For magicGNSS, the largest standard deviation was in the easting component, 9 cm greater than that of the up component. GAPS had the highest precision of the four providers in the northing component with a standard deviation of 1.7 mm. GAPS solution in the northing component had an approximate difference of 1cm from the reference solution. Due to GAPS having the lowest accuracy of the four PPP providers in the northing component but the highest precision indicates that there is a bias present in their solution. These results indicate that for 24 hour datasets PPP is capable of providing millimeter precision in northing, easting and up components.

**Table 4: Standard deviation of the PPP solution for 24 hour data arc. All units are in mm.**

## Convergence

In PPP, convergence is a major limitation due the relatively long period needed for a situation to reach a steady state. The Héroux et al. (2004) description of PPP convergence, it is dependent on several factors including: number and geometry of visible satellites, user environment and dynamics and observation quality. The varying convergence rate can be noted amongst figures 6 to 9 for the sites ALBH, NRC1, STJO and YELL, thus, affecting the time required to reach a defined precision for each site.

The segmented data for the four sites showed identical trends as expected, the least accurate was at the 1 hour data arc and most accurate at 24 hour data arc. The least accurate PPP processing was done by GAPS, this was most noticeable at the 1 hour data arc, after 6 hours its accuracy was comparable to APPS, CSRS-PPP and magicGNSS within 5 mm to 2 cm. For the 1 hour data arc, GAPS solution ranged between 26 cm and 40 cm amongst the four sites while the other three PPP processing software ranged between 1 cm and 12 cm. At site STJO, APPS solution had converged to 6mm for the 1 hour data block while CSRS-PPP was 11.5 cm and magicGNSS was 4.7 cm.

The four PPP software solutions for the four sites showed a decreasing exponential trend as the data arc increased from 1 to 24 hours as highlighted in figures 6 to 9 below. The most significant improvement in the accuracy of the solution was between 1 and 6 hour data arc. The solution improved by 1 cm to 15 cm for PPP providers CSRS-PPP, APPS and magicGNSS and 25 to 40 cm for GAPS. Increasing the data arc from 6 to 12 hours improved the solution by 1 mm to 2 cm amongst CSRS-PPP, GAPS and magicGNSS while APPS had the least improvement of the four sites ranging from 1 mm to 3 mm depending on the site. The improvement in accuracy of the solution ranged from 0.4 mm to 1.3 cm when the data arc was increased from 12 to 24 hours. GAPS had the largest improvement of the four PPP providers at ALBH and YELL of 1.1 cm and 1.3 cm respectively. The improvement in the solution ranged from 1 mm to 4 mm amongst the other providers.

The segmented data for the four sites showed identical trends as expected, the least accurate was at the 1 hour data arc and most accurate at 24 hour data arc. The least accurate PPP processing was done by GAPS, this was most noticeable at the 1 hour data arc, after 6 hours its accuracy was comparable to APPS, CSRS-PPP and magicGNSS within 5 mm to 2 cm. For the 1 hour data arc, GAPS solution ranged between 26 cm and 40 cm amongst the four sites while the other three PPP processing software ranged between 1 cm and 12 cm. At site STJO, APPS solution had converged to 6mm for the 1 hour data block while CSRS-PPP was 11.5 cm and magicGNSS was 4.7 cm.

The four PPP software solutions for the four sites showed a decreasing exponential trend as the data arc increased from 1 to 24 hours as highlighted in figures 6 to 9 below. The most significant improvement in the accuracy of the solution was between 1 and 6 hour data arc. The solution improved by 1 cm to 15 cm for PPP providers CSRS-PPP, APPS and magicGNSS and 25 to 40 cm for GAPS. Increasing the data arc from 6 to 12 hours improved the solution by 1 mm to 2 cm amongst CSRS-PPP, GAPS and magicGNSS while APPS had the least improvement of the four sites ranging from 1 mm to 3 mm depending on the site. The improvement in accuracy of the solution ranged from 0.4 mm to 1.3 cm when the data arc was increased from 12 to 24 hours. GAPS had the largest improvement of the four PPP providers at ALBH and YELL of 1.1 cm and 1.3 cm respectively. The improvement in the solution ranged from 1 mm to 4 mm amongst the other providers.

**Figure 6: 3D difference for ALBH with varying data arcs Figure 7: 3D difference for NRC1 with varying data arcs**

**Figure 8: 3D difference for STJO with varying data arcs Figure 9: 3D difference for YELL with varying data arcs**

The northing, easting and up components for the site ALBH are illustrated in Figures 10 to 12 below. Similarly, they all illustrated a decreasing exponential trend amongst all PPP providers. The most significant improvement was in the up component between 1 and 6 hour data arc for all PPP providers except CSRS-PPP at the site ALBH. The improvement ranged from 4 mm with CSRS-PPP to 25 cm with GAPS. The least significant difference was in the northing component ranging from 7mm to 1.3cm. The improvement in the easting component ranged from 4.29 cm to 9.28 cm amongst all PPP providers. From 6 to 12 hours the solution improved by 5 mm with APPS and 2.1 cm with GAPS in the up component. There was an improvement in the easting and northing component by 1 mm to 5 mm amongst all PPP providers. From 12 to 24 hours the solution improved by 1cm in the up component for GAPS and magicGNSS, while all other improvements ranged from 1mm to 4mm. It is difficult to easily identify convergence in PPP within the processed data arcs because the most significant convergence period of PPP occurs within the first 30 minutes of processing. The collection of more data would not improve the rate of convergence. This is dependent on how efficiently error sources are mitigated and how quickly the carrier phase ambiguity terms achieve a steady state.

**Figure 10: Easting component for ALBH with Figure 11: Northing component for ALBH**

**with**

**varying data arcs**

**varying data arcs**

**Figure 12: Up component for ALBH with varying data arcs**

## Precision of satellite orbit and clocks

Accurate orbits and clock products are critical for PPP processing if they do not meet the required accuracy it will not be possible to obtain an accurate PPP solution. Over the past 15 years the models used to determine precise orbits and clocks have been constantly improved. Selective Availability (SA) was switched off permanently on 2nd May 2000 and the 5 minute IGS satellite/station clock products became official on 5th November 2000 (Kouba, 2009).

The datasets examined range from 2000 to 2010 for 24 hour data arcs for the sites STJO, NRC1, ALBH and YELL. The datasets were chosen on January 1st of each year. The results were between 5mm and 4 cm from 2000 to 2010 for the four service providers. No PPP results were returned by magicGNSS and GAPS for the observation files used on 2000.0014 because there were no any high rate clock files available within their service. The magicGNSS and GAPS PPP software were unable to interpolate between the 15 minute clock intervals given in the SP3 file.

The accuracy of the results was expected to be directly proportional to time. This was not reflected in the results shown in figures 13 to 16. Table 5 below consists of the standard deviation and mean of the easting, northing and up components, and 3D difference. The standard deviation ranges from 6 mm to 19 mm in the easting, 3 mm to 11 m in the northing, 4 mm to 23 mm in the up component and 3 mm to 14 mm in the 3D difference. There was a mean (bias) in the 3D difference ranging from 1.11 cm to 2.7 cm amongst the four providers for the four sites. APPS had the lowest mean (bias) of the four providers for all sites except NRC1 where GAPS had the lowest. This is a strong indicator that the orbits and clocks use were reprocessed. This would also explain the high quality of results obtained for datasets before SA was turned off. The results indicate the importance of the quality and availability of high-rate precise orbits and clocks for PPP processing.

The datasets examined range from 2000 to 2010 for 24 hour data arcs for the sites STJO, NRC1, ALBH and YELL. The datasets were chosen on January 1st of each year. The results were between 5mm and 4 cm from 2000 to 2010 for the four service providers. No PPP results were returned by magicGNSS and GAPS for the observation files used on 2000.0014 because there were no any high rate clock files available within their service. The magicGNSS and GAPS PPP software were unable to interpolate between the 15 minute clock intervals given in the SP3 file.

The accuracy of the results was expected to be directly proportional to time. This was not reflected in the results shown in figures 13 to 16. Table 5 below consists of the standard deviation and mean of the easting, northing and up components, and 3D difference. The standard deviation ranges from 6 mm to 19 mm in the easting, 3 mm to 11 m in the northing, 4 mm to 23 mm in the up component and 3 mm to 14 mm in the 3D difference. There was a mean (bias) in the 3D difference ranging from 1.11 cm to 2.7 cm amongst the four providers for the four sites. APPS had the lowest mean (bias) of the four providers for all sites except NRC1 where GAPS had the lowest. This is a strong indicator that the orbits and clocks use were reprocessed. This would also explain the high quality of results obtained for datasets before SA was turned off. The results indicate the importance of the quality and availability of high-rate precise orbits and clocks for PPP processing.

**Table 5: Statistical comparison of precise orbits and clocks over a ten year period**

**Figure 13: 3D difference of 24 hour data arc for ALBH Figure 14: 3D difference of 24 hour data arc for NRC1**

**Figure 15: 3D difference of 24 hour data arc for STJO Figure 16: 3D difference of 24 hour data arc for YELL**

## Use of dual-frequency observables

When using pseudoranges, it is important to take into account the code biases in GPS. If the user does not match the observable to the one used to generate the corrections, significant precision degradation occurs (Collins et al., 2005). There are two ‘typical’ pairs of dual-frequency pseudorange observables, P1|P2 and C1|P2.

The data for the 4 sites, ALBH, NRC1, STJO and YELL were segmented into 1, 6, 12 and 24 hour data arcs and the P1 observable removed. This test was carried out to examine how efficiently the ionospheric errors were modelled using C1|P2 and the effects on the rate of convergence. Figures 17 and 18 below illustrate the 3D difference with and without the P1 observable for the 4 different data arcs processed by CSRS-PPP and APPS. This trend is similar amongst the four PPP providers with the most significant difference from the truth solution occurring at the 1 hour data arc. The difference in the quality of the solution was predominantly seen within the 1 hour data arc; this occurred because the solution was a pseudo-code solution. This indicates that the solution has not fully converged and the float ambiguities for the carrier phases have not been fully been resolved. There was one outlier within the processed data by APPS using C1|P2 dual-frequency. The least accurate solution was at the 12 hour data arc. The solution had a 3D difference of 10.8 cm as compared to the 1 hour data arc with a value of 1.1 cm and the 24 hour data arc with a value of 3 mm.

The effects of the dual-frequency pseudorange observables P1|P2 and C1|P2 for the 1 hour data arc for the different sites and PPP providers were analyzed. This is illustrated in Figures 19 to 21. It was expected that the C1|P2 would introduce a code bias as well as extend the convergence period because the ionosphere would not have been modelled as efficiently. The bias was prominent when processed by magicGNSS for sites ALBH, NRC1 and STJO with the largest bias occurring at STJO with a value of 11.7 cm and the smallest at NRC1 with a value of 15.3 cm. APPS illustrated this bias at ALBH and STJO with 10.9 cm and 1.1 cm respectively. For ALBH, STJO and YELL CSRS-PPP showed the results of the 3D difference being smaller when the C1|P2 was used. The difference of C1|P2 from P1|P2 for CSRS-PPP was minimal, at ALBH, STJO and YELL it was 1.4 cm, 3 mm and 5 mm respectively and at NRC1 the C1|P2 reproduced identical results as P1|P2. The bias introduced into the solution when using C1|P2 observables was expected to degrade the quality of the solution and extend the convergence period. The results varied amongst the PPP providers indicating that each provider corrected for the bias in the solution differently. The bias may have affected the convergence period but could not be truly appreciated by processing the 1 hour data arc because the most significant convergence period is within the first 30 minutes of processing.

The data for the 4 sites, ALBH, NRC1, STJO and YELL were segmented into 1, 6, 12 and 24 hour data arcs and the P1 observable removed. This test was carried out to examine how efficiently the ionospheric errors were modelled using C1|P2 and the effects on the rate of convergence. Figures 17 and 18 below illustrate the 3D difference with and without the P1 observable for the 4 different data arcs processed by CSRS-PPP and APPS. This trend is similar amongst the four PPP providers with the most significant difference from the truth solution occurring at the 1 hour data arc. The difference in the quality of the solution was predominantly seen within the 1 hour data arc; this occurred because the solution was a pseudo-code solution. This indicates that the solution has not fully converged and the float ambiguities for the carrier phases have not been fully been resolved. There was one outlier within the processed data by APPS using C1|P2 dual-frequency. The least accurate solution was at the 12 hour data arc. The solution had a 3D difference of 10.8 cm as compared to the 1 hour data arc with a value of 1.1 cm and the 24 hour data arc with a value of 3 mm.

The effects of the dual-frequency pseudorange observables P1|P2 and C1|P2 for the 1 hour data arc for the different sites and PPP providers were analyzed. This is illustrated in Figures 19 to 21. It was expected that the C1|P2 would introduce a code bias as well as extend the convergence period because the ionosphere would not have been modelled as efficiently. The bias was prominent when processed by magicGNSS for sites ALBH, NRC1 and STJO with the largest bias occurring at STJO with a value of 11.7 cm and the smallest at NRC1 with a value of 15.3 cm. APPS illustrated this bias at ALBH and STJO with 10.9 cm and 1.1 cm respectively. For ALBH, STJO and YELL CSRS-PPP showed the results of the 3D difference being smaller when the C1|P2 was used. The difference of C1|P2 from P1|P2 for CSRS-PPP was minimal, at ALBH, STJO and YELL it was 1.4 cm, 3 mm and 5 mm respectively and at NRC1 the C1|P2 reproduced identical results as P1|P2. The bias introduced into the solution when using C1|P2 observables was expected to degrade the quality of the solution and extend the convergence period. The results varied amongst the PPP providers indicating that each provider corrected for the bias in the solution differently. The bias may have affected the convergence period but could not be truly appreciated by processing the 1 hour data arc because the most significant convergence period is within the first 30 minutes of processing.

**Figure 17: CSRS-PPP dual-frequency solution for ALBH Figure 18: APPS dual-frequency solution for ALBH**

**Figure 19: 1 hour data arc dual-frequency solution Figure 20: 1 hour data arc dual-frequency solution**

**for ALBH**

**for NRC1**

**Figure 21: 1 hour data arc dual-frequency solution Figure 22: 1 hour data arc dual-frequency solution**

**for STJO**

**for YELL**