# Survey accuracy: The future of precision with 5 GNSS constellations

**Today’s GNSS satellites transmit on three or more carrier frequencies. The quality of the data in these signals from GPS, BeiDou, Galileo, GLONASS and QZSS reveals the expected measurement precisions. This article explores the noise of the range residual and ionospheric residual to indicate the oncoming capabilities.**

Today, four GNSSs transmit various codes on various carrier frequencies: the USA’s GPS, Russia’s GLONASS, Europe’s Galileo and China’s BeiDou. Most of the carrier phase and pseudorange data are available using civilian GNSS receivers. Improvements in signal quality as well as reliability of the satellites are foreseen through the generations, as well as the introduction of new signals, such as L1C, L2C, L5 carrier and codes, and M-codes, on top of the existing L1-C/A code and the P(Y) code on both L1 and L2. Improvements are also seen in boosting the transmitting power.

This article investigates the use of two approaches to analyze the relative noise in the various carrier phase and pseudorange observable for GPS, BeiDou, Galileo, GLONASS and Japan’s Quasi-Zenith Satellite System (QZSS) augmentation. Two approaches analyze the relative noise in the observables: the range residual and the ionospheric residual. Both techniques can also be used to detect cycle slips.

### Range Residual

The range residual is simply the change from one epoch to the next in the difference in the range calculated using the pseudorange and the range calculated by the carrier phase on a specific frequency. The pseudorange values are scaled using the wavelength to an equivalent range in units of the carrier’s cycles rather than meters. Equation 1 illustrates the range residual between the pseudorange ρ on a specific carrier frequency and the carrier phase observable φ, using the wavelength λ of the carrier to scale the pseudorange. The values of these observables are compared between adjacent epochs.

RR = (p/λ) – φ (1)

Two adjacent epochs are used, as then the integer ambiguity value, as well as the ionospheric and tropospheric errors, and satellite and receiver clock errors are the same, or negligibly different at such small (<1 s) epoch intervals. Therefore, these are all canceled out, and the resulting value is the measurement receiver and observable noise. The pseudorange observable will be significantly noisier than the carrier phase observable, therefore this method is a good way to calculate the measurement noise for the pseudoranges.

### Ionospheric Residual

If the carrier waves traveled only through a vacuum, then a phase observation from a specific satellite to a specific GNSS receiver could be scaled and converted to an equivalent phase measurement on another frequency using the frequencies of the carrier waves. However, as the signal passes through the ionosphere, systematic errors that are frequency dependent are introduced, so it is not possible to directly convert from one carrier phase value to another for a specific range measurement. The error is known as the ionospheric residual, and this will change slowly over time as the satellite passes overhead and the ionosphere being passed through changes, and also as the ionosphere slowly changes its characteristics over time, mainly due to the sun’s activities.

Equation 2 shows the calculation, using L1 and L2 carrier phase readings and corresponding frequencies, used to calculate the ionospheric residual. Again, the difference in the ionospheric residual values between adjacent epochs is used, as in the same way as the range residual values, external noise sources are eliminated.

### Results

The results presented here are a subset of a much larger set. Figure 1 illustrates the range residuals for L1 and L2 as well as the L1L2 ionospheric residual for PRN32 (Block IIA satellite).

Figure 2 illustrates the L1 and L5 range residuals and the L2 (C-code) L5 ionospheric residual for PRN01 (Block IIF satellite).Both figures’ data are for the complete passing of the satellites from horizon over and back down again.The data for PRN32 is all that exists in the datafile, as this satellite only transmits L1 CA code and P(Y) code, as well as L2 P(Y) code, and corresponding carrier values.

PRN01 is a block IIF satellite, and data for L1 CA code, L2 P(Y) code as well as L2 C-code, L5 code, and corresponding carrier phase values are recorded in the datafile.The block IIF satellites can result in four range residual values and five ionospheric residual combinations.Figure 2 only illustrates three of these combinations.The data were obtained from the Curtin University GNSS repository on Sept. 1, 2015, gathered at a 1-Hz epoch interval; 29,908 epoch of data were gathered for PRN32, and 26,073 epochs for PRN01.

It can be seen from these figures that the L1 range residuals are similar in characteristics for both PRN01 and PRN32.The values are noisy at the start and the end of the time series, indicating that the CA code is more prone to noise at low elevations.Comparing these to the L2 (PRN32) and L5 (PRN01) range residuals, we can see that both the L2 and L5 range residuals are not as prone to low elevation noise. Also, the two L2 and L5 range residuals are visually similar in characteristcs.By comparing the L1L2 and L2L5 ionospheric residuals (Figure 1, right, and Figure 2, right), we can see that the L1L2 combination is slightly noisier than the L2L5, in particular at low elevation angles.

If we compare BeiDou ionospheric residual results, we can see the comparison of noise on the three ionospheric residual combinations, B1B2, B1B3 and B2B3, as well as the results from the three types of satellite orbits, ie MEO, IGSO and GEO. Figure 3 illustrates the ionospheric residual results for PRN07 (IGSO) for the three frequency combinations, from data gathered on a static pillar located on top of the University of Nottingham Ningbo China’s Science and Engineering Building.

Figure 4 illustrates the ionospheric residual results for PRN01 (GEO) for the three frequency combinations.

Figure 5 illustrates the ionospheric residual results for PRN12 (MEO) for the three frequency combinations. Here it can be seen that the B2B3 combination is generally less noisy than the B1B2 and B1B3. In addition to this, it can be seen that when the MEO and IGSO satellites are at lower elevation angles, the observables also become noisier. The GEO satellites have a constant elevation angle, and do not experience this phenomenon.

### Detailed Results

The data, gathered on a single GNSS receiver located at the University of Curtin’s GNSS research center, was downloaded in BINEX format and converted into RINEX 3.02 format using RTKLIB software. Software was developed by the authors in Matlab in order to interrogate the data files and implement the range residual and ionospheric residual algorithms. RINEX 3.02 format was chosen due to its compatibility with multi-GNSS and multi-frequencies.

Results are presented for both ionospheric residual and range residual results for various GNSS. These results have been calculated with varying elevation mask angles, ranging from 0° to 55° at 5° intervals. The RMS values of the resulting ionospheric residuals and range residuals were calculated and plotted against the respective elevation mask angle for each satellite and frequency combinations. This illustrates the influence of the elevation mask angle used on the results.

Typically, tens of thousands of epochs of data were used for every plotted point in the following figures. Further to this, not only are the results for the various frequencies and frequency combinations for the various GNSS illustrated, but also the various satellite types, MEO, GEO and IGSO, and various satellite Blocks for GNSS. GPS Block IIA (PRN04 and PRN32), Block IIR (PRN14), Block IIR-M (PRN31) and Block IIF (PRN01, PRN26, PRN25) data were all analyzed. Thus, the comparison of the various frequencies within each satellite system are illustrated, as well as the variations by comparing the various satellite constellation types and the various generations of GPS satellites.

The BeiDou data illustrated are MEO (C12, C14, C11), IGSO (C09, C10, C07) and GEO (C01, C02). The data used were gathered on Sept. 1, 2015, in order to include GPS Block IIA satellites (PRN04 and PRN32). PRN32 was retired in June 2016, and PRN04 was taken out of active service in November 2015, but the satellite was reactivated in March 2018, this time broadcasting PRN18.

Figure 6 illustrates RMS of the range residual results for GPS (a), BeiDou (b), Galileo (c), GLONASS (d) and QZSS (e) respectively. These figures have been drawn so that the y-axis ranges are the same for each, hence illustrating the relative values.

Figure 6A illustrates the range residual results for GPS. It can be seen that the L1 CA code results are the noisiest, with PRN14 being the noisiest, followed by PRN31, PRN26, PRN01, PRN04, PRN25 and PRN32. It can also be seen with these results that lower elevation angle mask increases the noise level. Both the L2 and L5 code results are less noisy.

Looking at the detail, the L5 code results is less noisy than the L2 and affected less than the L1 results by the changes in elevation mask angles used. Interestingly enough, the data file includes both the L2 P(Y) code and L2C code results. L2C only exists on the Block IIR-M and Block IIF satellites. The L2C code results are generally noisier than the L2 P(Y) code.

Figure 6B illustrates the results for the range residuals for the BeiDou satellites. Here it can be seen that the B1 code is affected more by low elevation mask angles than B2 and B3. It can also be seen that both the geostationary satellites’ B1 results stand out, with satellite C02 being noisier than C01. The B2 and B3 values for both these GEO satellites are bunched up with the majority of the other results towards the middle of the figure. The pairs of B2 and B3 results for the GEO satellites are close to each other in values, and the pairs of B2 and B3 results for the other satellites are also close to each other.

It can also be seen that the range residual results for BeiDou are generally less noisy than than GPS, in units of cycles.

Similarly, for Galileo, Figure 6C, the E1 results are worst, and affected more by low elevation masks. Again, generally the Galileo results are seen to be improved over GPS. The GLONASS results, Figure 6D, illustrate that the L1C results are generally noisier, and then the L1P, followed by L2C and L2P. PRN09 is also consistently generally noisier than PRN10. Finally, Figure 6E illustrates the results for QZSS. Again, L1C is the noisiest and affected most by low elevation mask angles.

Figure 7 illustrates the ionspheric residual results for the same satellites as Figure 6. This time, however, the resulting ionospheric residual values are calculated using pairs of data from the same satellite on different carrier frequencies. The range residual results compare the code and carrier from specific satellites and frequencies.

Figure 7(a) shows that the ionospheric residual results are affected by low elevation masks, and that the L1L2CW (L1 CA code and L2 P(Y) code available on all the satellites) combinations are the noisiest, followed by L2L5WX (L2 P(Y) code and L5 code available on Block IIF satellites, PRN 26, PRN01, PRN25), followed by L1L2CX (L1 CA code and L2 C code available on Block IIF and Block IIR-M satellites, PRN31, PRN26, PRN01 and PRN25), followed by L1L5CX (L1 CA code and L5 code, Block IIF satellites, PRN01, PRN25, PRN26) and finally the least noisy were the L2L5XX results (L2 C code and L5 code available on Block IIF satellites, PRN26, PRN25 and PRN01).

Figure 7(b) illustrates the BeiDou ionospheric residual plots, illustrating that satellite C14 is much noisier for all three combinations of B1B3, BB1B2 and B2B3 in that order. The B1B2 combinations for the satellites are generally the noisiest, and then the B1B3 and B2B3 combinations are intertwined. The Galileo results again illustrate that the E1 combinations are generally noisier, and again we see the effect of low elevation angle masks, Figure 7(c). Generally, however, the Galileo results are less noisy than GPS, as are the BeiDou results.

The GLONASS results are again generally the noisiest, and again PRN09 is noisier than PRN10, with the L1P combinations being noisier, Figure 7(d). Figure 7(e) for QZSS shows that there are generally two groups of results. The upper set consists of L1L2ZX, L1L5ZX, L1L2XX, L1L5XX, L1L6ZX and L1L6XX from highest to lowest noise respectively. The lower, less noisy, group consists of L1L2CX, L1L5CX, L2L5XX, L2L6XX, L1L6CX and L5L6XX from highest to lowest noise respectively. Further details about the various codes and carrier values can be found in the RINEX 3.02 manual produced by the IGS.

### Conclusions

These preliminary results illustrate that there are differences in the noise values for various GNSS, frequencies as well as satellite generations and orbit types. It can be seen that generally L1, B1 and E1 have noisier results, and are affected moreso by low elevation mask data, and hence multipath. It can also be seen that newer generations of satellites do indeed produce better quality data.

Some specific satellites produce lower quality data such as GLONASS PRN09 and BeiDou C14. This could be due to multipath produced at the satellite.

Today roughly 100 GNSS transmit data, and typically users can gather data from 30 to 50 at any time. Positioning requires nowhere near this number of satellites, therefore decisions are needed as to which satellites and which data to use in a positioning solution. Our findings imply that our approach could be used in such decision-making in GNSS processing software, helping the software to choose the optimum satellites to draw from in a positioning solution.

### Acknowledgments

This work described in this article was first presented at the FIG 2018 conference held in Istanbul, Turkey. The authors acknowledge the use of data supplied from the Curtin University GNSS Centre.

### Manufacturers

The GNSS receiver used is a Trimble NET R9, and the antenna is a Trimble TRM 59800.00 SCIS choke ring antenna. A ComNav K508 GNSS receiver supplied some of the BeiDou results.

*GETHIN WYN ROBERTS is an associate professor at Fróðskaparsetur, the University of the Faroe Islands. He is past Chairman of the FIG’s Commission 6, Engineering Surveys, and previously held posts at the University of Nottingham both in the UK and in China. He holds a Ph.D. in engineering surveying and geodesy from the University of Nottingham.*

*CRAIG M. HANCOCK is an associate professor in Geodesy and Surveying Engineering and the head of the Department of Civil Engineering at the University of Nottingham, Ningbo, China as well as the head of the Geospatial and Geohazards Research Group. He holds a PhD from the University of Newcastle Upon Tyne.*

*XU TANG is a research fellow at the University of Nottingham, Ningbo, China. He holds a PhD from Nanjing University.*

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