ON GLONASS pseudo-range inter-frequency bias solution with ionospheric delay modeling and the undifferenced uncombined PPP

Abstract

With the development of multi-GNSS, the differential code bias (DCB) has been an increasing interest in the multi-frequency multi-GNSS community. Unlike code division multiple access (CDMA) mode used by GPS, BDS and Galileo etc., the GLONASS signals are modulated with frequency division multiple access (FDMA) mode. Up to now, the FDMA-aware GLONASS bias products are provided by two individual IGS analysis center (AC), i.e., CODE and GFZ. However, only the ionosphere-free (IF) combination IFB of P1 and P2 is available, while it is founded that the GLONASS IFB of GFZ on both frequencies are identical for the same receiver-satellite pair. In this contribution, the GLONASS IFB (inter-frequency bias) solution based on the spherical-harmonic (SH) ionospheric delay modeling as well as the undifferenced and uncombined PPP were carried out and evaluated. Based on the theoretical analysis, observations from 236 CMONOC stations and 172 IGS stations were collected for 2014 March and 2017 March for the numerical verification. The results suggested that the precision of IFB estimates was mainly subjected to the ionospheric status. Concerning the SH ionospheric delay modeling solution, the STD was 0.85 ns and 0.51 ns for 2014 and 2017, respectively. Concerning the undifferenced and uncombined PPP solution, the IFB was further dependent on the signal frequencies, and the STD was 1.43 ns and 1.94 ns for ${\mathrm{IFB}}_{1}$ and ${\mathrm{IFB}}_{2}$ in 2014, and the STD was 0.97 ns and 1.17 ns for ${\mathrm{IFB}}_{1}$ and ${\mathrm{IFB}}_{2}$ in 2017. When converted to the GF IFB from the individual IFB on each frequency, and compared to that of GF IFB of SH solution, it is revealed that the undifferenced and uncombined PPP solution has its advantages for IFB estimation on each individual frequency, and more efficient in data processing, while the solution based on the SH ionospheric delay modeling has its advantage in the precision of the GF IFB estimates. Thus, it is suggested that the SH model should be preferred for non-time-critical GF IFB concerned-only applications. Otherwise, the undifferenced and uncombined PPP solution is preferred. These IFB on each frequency was further converted to the ionosphere-free IFB and compared with the products of CODE analysis center.

Appendix

In this part, details of each receiver-satellite pair IFB were presented. Figures 15, 16, 17 and 18 present the GF IFB of CMONOC for March 2014, CMONOC for March 2017, IGS for March 2014 and IGS for March 2017 with the SH ionospheric delay modeling solution. Figures 19, 20, 21 and 22 present the IFB on each individual frequency of CMONOC for March 2014, CMONOC for March 2017, IGS for March 2014 and IGS for March 2017 with the PPP ionospheric delay modeling solution. Figures 23, 24, 25 and 26 present the GF IFB of CMONOC for March 2014, CMONOC for March 2017, IGS for March 2014 and IGS for March 2017 with the PPP ionospheric delay modeling solution.

Fig. 15

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for CMONOC stations in March 2014 based on the SH ionospheric delay modeling solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.78 ns

Fig. 16

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for CMONOC stations in March 2017 based on the SH ionospheric delay modeling solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.50 ns

Fig. 17

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for IGS stations in March 2014 based on the SH ionospheric delay modeling solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.92 ns

Fig. 18

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for IGS stations in March 2017 based on the SH ionospheric delay modeling solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.52 ns

Fig. 19

The mean value (a) and the STD (b) for GLONASS IFB (1: ${\mathrm{IFB}}_{1}$; 2: ${\mathrm{IFB}}_{2}$) of each receiver-satellite pair for CMONOC stations in March 2014 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 1.73 ns

Fig. 20

The mean value (a) and the STD (b) for GLONASS IFB (1: ${\mathrm{IFB}}_{1}$; 2: ${\mathrm{IFB}}_{2}$) of each receiver-satellite pair for CMONOC stations in March 2017 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 1.06 ns

Fig. 21

The mean value (a) and the STD (b) for GLONASS IFB (1: ${\mathrm{IFB}}_{1}$; 2: ${\mathrm{IFB}}_{2}$) of each receiver-satellite pair for IGS stations in March 2014 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 1.64 ns

Fig. 22

The mean value (a) and the STD (b) for GLONASS IFB (1: ${\mathrm{IFB}}_{1}$; 2: ${\mathrm{IFB}}_{2}$) of each receiver-satellite pair for IGS stations in March 2017 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 1.107 ns

Fig. 23

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for CMONOC stations in March 2014 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 1.11 ns

Fig. 24

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for CMONOC stations in March 2017 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.63 ns

Fig. 25

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for IGS stations in March 2014 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.94 ns

Fig. 26

The mean value (a) and the STD (b) for GLONASS IFB (${\mathrm{IFB}}_{\mathrm{GF}}$) of each receiver-satellite pair for IGS stations in March 2017 based on the undifferenced and uncombined PPP solution. The X-axis is grouped according to the receiver type. The color bar represents the STD value in ns, and the averaged STD is about 0.59 ns