On the satellite clock datum stability of RT-PPP product and its application in one-way timing and time synchronization

Abstract

In real-time precise point positioning (RT-PPP), PPP one-way timing is used to steer local oscillators, but the timing performance could be significantly affected by the datum stability of the satellite clock product. To measure the stability of a satellite clock datum relative to the hydrogen maser (H-MASER) clock, a new GNSS satellite clock datum stability assessing model based on the overlapping Allan variance (AVAR) is proposed for both PPP one-way timing and time synchronization. Experiments were carried out with nine Global Navigation Satellite System (GNSS) stations at time laboratories with an external H-MASER clock to analyze the datum stability performance. In the experiments, RT satellite products from five RT Analysis Centers (ACs): CNES, ESA, GFZ, GMV, WHU, and the final satellite product from IGS were used in the comparison. Results show that the datum stability of all RT products tended to be similar, i.e., 6 to 8E−15/day, where WHU and GMV outperformed other RT ACs. Moreover, these datum stability results indicate that RT-PPP for steering local oscillators improves stability to 6 to 8E−15/day when selected with an appropriate RT product. The estimation noise in all RT ACs was at about the same level, i.e., 1 to 2E−15/day, but WHU delivered the most stable performance. Thus, datum stability is an effective guide for setting parameters and making long-term stability predictions when steering local oscillators, and satellite clock datum stability can be measured conveniently and quickly using the GNSS satellite clock datum stability assessing model proposed in this paper.

Appendices

Appendix A

The satellite clock double difference, i.e., the difference between WHU RT product and IGS final product, and further between satellites, from DOY (day of the year) 016, 2022 is presented in Fig. 7 to show the existence of ${t}_{0}^{{s}_{i}}$ (Yao et al. 2017). As shown in Fig. 7, ${t}_{0}^{{s}_{i}}$ is rather stable.

Fig. 7

The satellite clock double difference from DOY 016, 2022 with WHU and IGS

Appendix B

To confirm that the cross-term of two independent power law clock noise with a similar noise parameter is one or two orders lower than the Allan deviation of each term, we used Stable32 software (http://www.wriley.com/) to generate a noise sequence n1 and n2 with the strategy of Table

Table 5 Noise generative strategy

5.

Where $\tau$ represents the average time, $N$ is the number of points, WPM is White Phase Modulation Noise, FPM is Flicker Phase Modulation Noise, WFM is White Frequency Modulation Noise, FFM is Flicker Frequency Modulation Noise, and RWFM is Random Walk Frequency Modulation Noise. The power law noises mentioned have a specific power spectral density of their fractional frequency fluctuations of the form ${\mathrm{S}}_{\mathrm{y}}\left({f}\right)\propto {{f}}^{\mathrm{a}}$, where $f$ is the Fourier or sideband frequency in hertz; and $a$ is the power law exponent. The $a\, {\text {of}}\, \mathrm{WPM},\mathrm{ FPM},\mathrm{ WFM},\mathrm{ FFM},\mathrm{ and\, RWFM\, are }\,2, 1, 0, -1,\mathrm{ and }-2.$

The Overlapping Allan deviation graph of n1, n2, and cross-term of n1 and n2 was as follows:

As shown in Fig. 8, the cross-term was about one order lower than that of the two origin random noises, i.e., n1 and n2. Note that the cross-term is not always positive, and the log–log diagram only presented the positive sequence.

Fig. 8

Overlapping Allan deviations of n1, n2, and cross-term of n1 and n2

In order to explain the effect of the cross-term between the reference and the noise on the reference, we simulate the similar overlapping Allan deviation curve by our experiment result and give the simulation parameters in Table

Table 6 Reference and Noise generative strategy

6.

We generate a noise sequence r and n as reference and noise. The Overlapping Allan variance graph of r, n, and the cross-term of r and n was as follows (Fig. 9).

Fig. 9

Overlapping Allan deviation s of r, n, and cross term of r and n

The effect of the cross-term on reference needs to be discussed here because the noise has been detached from the reference. From the simulation results, the cross-term on the impact of the reference is minimal.