GNSS Constellation Specific Monthly Analysis Summary: July 2024

Sep 2024 | No Comment

The analysis performed in this report is solely his work and own opinion. State Program: U.S.A (G); EU (E); China (C) “Only MEO- SECM satellites”; Russia (R); Japan (J); India (I)

Narayan Dhital

Actively involved to support international collaboration in GNSSrelated activities. He has regularly supported and contributed to different workshops of the International Committee on GNSS (ICG), and the United Nations Office for Outer Space Affairs (UNOOSA). As a professional employee, the author is working as GNSS expert at the Galileo Control Center, DLR GfR mbH, Germany

Introduction

The article is a continuation of monthly performance analysis of the GNSS constellation. In this month’s issue, there is an additional discussion on the periodicity of the satellite atomic clock offset.

Analyzed Parameters for June, 2024

(Dhital et. al, 2024) provides a brief overview of the necessity and applicability of monitoring the satellite clock and orbit parameters.
a. Satellite Broadcast Accuracy, measured in terms of Signal-In-Space Range Error (SISRE) (Montenbruck et. al, 2010).
b. SISRE-Orbit ( only orbit impact on the range error), SISRE (both orbit and clock impact), and SISRE-PPP (as seen by the users of carrier phase signals, where the ambiguities absorb the unmodelled biases related to satellite clock and orbit estimations. Satellite specific clock bias is removed) (Hauschlid et.al, 2020)
c. Clock Discontinuity: The jump in the satellite clock offset between two consecutive batches of data uploads from the ground mission segment. It is indicative of the quality of the satellite atomic clock and associated clock model
d. URA: User Range Accuracy as an indicator of the confidence on the accuracy of satellite ephemeris. It is mostly used in the integrity computation of RAIM.
e. GNSS-UTC offset: It shows stability of the timekeeping of each constellation w.r.t the UTC
f. Satellite Clock Offset Fourier Analysis: The knowledge of a periodic behavior of the on-board atomic clock offset is essential for better prediction model.

Note:- for India’s IRNSS there are no precise satellite clocks and orbits as they broadcast only 1 frequency which does not allow the dual frequency combination required in precise clock and orbit estimation; as such, only URA and Clock Discontinuity is analyzed.

(f) Satellite Clock Offset Fourier Analysis

The atomic clocks on-board satellites are influenced by various phenomena such as the J2 term, Earth oblateness, satellite thermal radiation, and estimation errors induced by satellite orbits. These periodic variations in the satellite clock data are often absorbed by the satellite clock offset, resulting in periodic signals if not properly modeled. A quadratic polynomial fit (QPM) of the reference satellite clock offset serves as a starting point for analysis. The residuals of the QPM for different satellites and atomic clock types reveal variations due to differing orbits.

A simple Fast Fourier Transform (FFT) analysis highlights these periodic components. For Medium Earth Orbit (MEO) satellites like GPS, GAL, and BDS, the twice-per-day term is prominent, reflecting their MEO orbit period. In contrast, Geostationary Earth Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO) satellites (C04 and C10, respectively) exhibit different periodic terms. For GEO satellites, the dominant term is the 1 cycle per day, with its harmonics decreasing in strength with integer multiples.

The plots in Figure f(a) and f(b), visually represents these periodicities. The time series of the residuals (f(a)) obtained by subtracting the satellite clock offset from the QPM predicted values show distinct oscillations for Beidou IGSO and GEO on-board atomic clock. For atomic clocks on-board the MEO orbit the residuals are not stark. However, G08 shows a lot of noise and variation in the residuals and this is due to the Cesium frequency standard used in G08, for which linear model is more suitable than the QPM. The significant peaks at specific frequencies (in f(b)) indicate the presence of pronounced periodic components in the satellite clock offsets. These peaks correspond to the periodic terms discussed, with MEO satellites showing strong twice-per-day components and GEO satellites displaying daily cycles and their harmonics.

The temporal variation of amplitudes and the prime frequency components for satellites are crucial for understanding the stability and accuracy of satellite clocks. Temporal variations can indicate changes in the satellite’s environment or operational conditions, which can affect the clock’s performance. By analyzing these variations, constellation service provider can identify and mitigate potential sources of error.

Short-Time Fourier Transform (STFT) can be used to analyze these temporal variations by providing a time-frequency representation of the signal. STFT allows for the observation of how the frequency components of the satellite clock offsets change over time, offering a more detailed understanding of the periodic effects. This analysis helps to better solidify the clock model by identifying transient behaviors and ensuring that the model accurately reflects the satellite’s performance over its operational period. In general, the GNSS satellite atomic clocks demonstrate the temporal variation in amplitude and frequency. The assessment of such variations and in-dept periodicity analysis of different satellite atomic clocks will be provided in the future issue of the article.

Figure f (b): The FFT of the QPM residuals for different satellite atomic clocks flying on various satellite orbits. As the time period of the analysis is only 11 days (Jan 9-20,2021, GFZ Final Clocks), the primary components might not be reflected properly. The longer the time period for FFT analysis, the better the resolution and detection of correct components. The FFT in this context is mostly to serve the residuals analysis in f(a).

Monthly Performance Remarks:
1. Satellite Clock and Orbit Accuracy:
• For GPS, the satellite clock and orbit accuracy shows slight performance improvement.
• For Galileo, all parameters showed consistent performances. Satellite E12 has a large clock jump on DOY 203 around 18:00 UTC. There was a missing BRDC data for 1 hour and right afterwards the satellite was set to NAPA. Further check is needed as it could be a near fault event.
• For GLONASS, the performance looked similar to the past months.
• For BDS and QZSS, the performance looks very much the same as in the past.
• For IRNSS, the notable difference in this month’s performance is the URA for I03. There is no broadcast record. For I02 and I06, a new URA value of 11.3 was recorded.

2. UTC Prediction (GNSS-UTC):
• High osscillation of GPS-UTC between DOY 208-2013. GLONASS had large offset that started to decrease after DOY 189 and reached finally within 5 ns level.

References

Alonso M, Sanz J, Juan J, Garcia, A, Casado G (2020) Galileo Broadcast Ephemeris and Clock Errors Analysis: 1 January 2017 to 31 July 2020, MDPI

Alonso M (2022) Galileo Broadcast Ephemeris and Clock Errors, and Observed Fault Probabilities for ARAIM, Ph.D Thesis, UPC

Cao X, Zhang S, Kuang K, Liu T (2018) The impact of eclipsing GNSS satellites on the precise point positioning, Remote Sensing 10(1):94

Dhital N (2024) GNSS constellation specific monthly analysis summary, Coordinates, Vol XX, Issue 1, 2, 3, 4

Hauschlid A, Montenbruck O (2020) Precise real-time navigation of LEO satellites using GNSS broadcast ephemerides, ION

Guo F, Zhang X, Wang J (2015) Timing group delay and differential code bias corrections for BeiDou positioning, J Geod,

IERS C04 (2024) https://hpiers.obspm.fr/ iers/eop/eopc04/eopc04.1962-now IGS (2021) RINEX Version 4.00 https://files.igs. org/pub/data/format/rinex_4.00.pdf

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Liu T, Chen H, Jiang Weiping (2022) Assessing the exchanging satellite attitude quaternions from CNES/CLS and their application in the deep eclipse season, GPS Solutions 26(1)

Montenbruck O, Steigenberger P, Hauschlid A (2014) Broadcast versus precise ephemerides: a multiGNSS perspective, GPS Solutions

Montenbruck O, Hauschlid A (2014 a) Differential Code Bias Estimation using Multi-GNSS Observations and Global Ionosphere Maps, ION

Steigenberger P, Montenbruck O, Bradke M, Ramatschi M (2022) Evaluation of earth rotation parameters from modernized GNSS navigation messages, GPS Solutions 26(2)

Sylvain L, Banville S, Geng J, Strasser S (2021) Exchanging satellite attitude quaternions for improved GNSS data processing consistency, Vol 68, Issue 6, pages 2441-2452

Walter T, Blanch J, Gunning K (2019) Standards for ARAIM ISM Data Analysis, ION

Wang N, Li Z, Montenbruck O, Tang C (2019) Quality assessment of GPS, Galileo and BeiDou-2/3 satellite broadcast group delays, Advances in Space Research

Note: References in this list might also include references provided to previous issues.