GNSS Constellation Specific Monthly Analysis Summary: January 2025

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. Please refer to previous issues for past analysis. Regarding applications, there was an interpretation and discussion in the last month’s issue on the usage of GNSS PVT solutions for the Terminal Area Energy Management of spaceplanes, re-usable space vehicles and unmanned air vehicles. In this article it will be further elaborated with a real-data analysis combining GPS and IMU data.

Analyzed Parameters for January, 2025

(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-InSpace 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. GNSS-IMU Coupling: Coupling of the GNSS and IMU is a standard procedure in avionics. The benefit of each technology is realized through various architectures and algorithms. It helps to have a robust navigation solutions even during satellite outages, and fault events.

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.

Note: The author is an experienced air navigation engineer with flight deck experience in assessing the navigation performance of the aircraft. The analysis below is based on the public resources and not directly from author’s work due to ethic and contractual reasons.

In the article issued in January 2025 (Dhital et.al, 2025), the application of GNSS in the navigation of aircraft, launcher and re-entry vehicle was discussed. A couple of real-life operational examples were provided to highlight the capabilities of GNSS for safe, secured and efficient navigation of such vehicles. This article focuses on the data analysis to provide further understanding of operational benefits provided by GNSS in the frame of GNSS and IMU integration. The results are correlated to the operational examples provide in the January’s issue.

The fused solution of GNSSs (although only GPS is used in the aircraft FMS as of now) and IMUs provide reliable solution taking benefits of both GNSS and IMU. Using an open-source software “GINav” (Chen et,al. 2021), it is demonstrated that GNSS+IMU provides better solution than either of the individual solution. The complexity of the fused algorithm in the aircraft plays a greater role in the robustness of the solution. Even though, in commercial aviation, the aircraft have varying degrees of GPS and IMU coupling depending on the model, this article provides the analysis on the characteristics of only loosely coupled and tightly coupled GPS and IMU. The mathematical description and analysis are not the scope here, however, and the references (Chen et.al, 2021), (Liu et.al, 2018), (Wang et.al, 2025), (Bento et.al, 2013) and (Goercke et.al, 2017) provide a good detail on the topic.

The procedures for the data analysis are based on the following steps:
1. Only GPS is selected as the GNSS constellation, because only GPS is certified for aircraft FMS. The GPS solution is based on the Single Point Positioning (SPP). To compute position, velocity and attitude (roll, yaw and pitch). Note: the attitude values are also used in the fly-by-wire control of the aircraft lateral and longitudinal aerodynamics.
2. IMU stand-alone solution is computed through the mechanization equations
3. IMU aided by GPS solution is computed. This is based on loosely coupled mode where two separate Kalman filters are used for each of the IMU and GPS solution which are then combined.
4. Some epochs are refined to remove a couple of GPS satellites (total number of satellites below 4). This means GPS standalone solution is not possible. (This is called Data modification 1)
5. Using the data from step 4, the IMU aided by GPS solution in loosely coupled mode is computed.
6. Using the data from 4, the tightly coupled IMU+GPS solution is computed
7. The innovation (residuals between the IMU predicted and GPS measurements) is computed for step 5 8. The figure of merit for above 5 and 6 is computed.
9. A fake GPS measurement data is used for a couple of epochs. (This is called Data modification 2)
10.The loosely coupled solution for using data from step 9 is computed. The innovation residual of the GPS filter is used for Chi-square statistics test.

Data source: The publicly available dataset from the github (GINav/data at main · kaichen686/GINav · GitHub), which is collected in a suburban environment around the university of Mining and Technology, China, on March 28, 2019 is used. The data collection platform is equipped with the Trimble R10 receiver and a tactical grade IMU, together with accurate reference solutions from NovAtel-SPAN-CPT system.

Data modification 1: The GNSS data is changed by removing couple of satellites (keeping number of satellites below 4) for some epochs to disable GNSS solution computation. This is to check the performance of LC and TC modes during satellite outages.

Data modification 2: The GNSS data is changed by adding fake measurement data for few epochs. This is to check the innovation residuals and chi-square statistics to detect anomalies and outliers.

Before starting the data analysis and interpretation, a very high-level understanding of the GNSS+IMU integration is provided below:

Dynamic Models

The dynamic model describes how the system state evolves over time. In GNSS/IMU integration, the state vector typically includes position, velocity, attitude, and IMU biases (accelerometers and gyroscopes). The state transition model explains how these elements change over time, incorporating the effects of motion and sensor measurements.

IMU Mechanization

IMU mechanization involves using accelerometer and gyroscope measurements to update the position, velocity, and attitude of the aircraft. The position and velocity are updated based on the accelerations, while the attitude is updated using the angular rates from the gyroscopes. This process ensures continuous tracking of the aircraft’s movement, even when GNSS signals are unavailable. The core of the mechanization process involves solving the equations of motion.

Accelerometers measure linear acceleration by detecting the Coriolis force acting on a vibrating mass inside the sensor. Similarly, gyroscopes measure angular velocity by detecting the Coriolis force acting on a vibrating mass inside the sensor. For sensors based on laser/optics, Sagnac effect is considered in the mechanization.

The dynamics model and IMU mechanization (which uses high grade laser/optical sensors) are a bit complex for aircraft. (Bruggemann et.al, 2011) provides some overview on it.

GNSS Measurement Models

GNSS measurements include pseudoranges, carrier phases, and Doppler shifts. These measurements provide information about the distance between the satellites and the receiver, which is used to update the state estimate. The pseudorange measurement model calculates the distance based on the time it takes for the GNSS signal to travel from the satellite to the receiver.

State-Space Model

The state-space model combines the dynamic model and the measurement model to estimate the state vector. The measurement update step involves comparing the observed measurements with the predicted measurements to calculate the measurement residuals (innovations). These residuals are then used in the form of a filter gain to correct the state estimate, improving the accuracy of the navigation solution.

Loosely Coupled vs. Tightly Coupled Integration
• Loosely Coupled (LC): In this approach, GNSS and IMU data are processed separately. The GNSS solution is used to correct the IMU solution. The EKF is implemented separately for GNSS and IMU and then individual solution is combined in another EKF. This method is simpler and less computationally intensive but may be less accurate in challenging environments where GNSS signals are weak or unavailable.
• Tightly Coupled (TC): In this approach, raw GNSS measurements are directly integrated with IMU data in the Kalman filter. The pseudorange and dopplers are predicted based on the IMU data and the last know GNSS satellites and bias values. This is than updated with the obtained measurements of pseudo range and dopplers. The method provides more accurate and robust navigation solutions, especially in environments with limited GNSS visibility, but it is more complex and computationally demanding.

Robustness of the Kalman filter:

In the LC mode, the IGG-3 robust model is used to down-weight or exclude outliers in the innovation residuals for the GPS/ IMU mode. It calculates the standard residuals, applies robust factors to adjust the measurement noise covariance matrix, and removes measurements with high residuals, ensuring the integrity and robustness of the state estimation.

Results and Discussions:

InFigure F1, the characteristics of IMU only, GPS only and the IMU+GPS integration are demonstrated. The drifting nature of the IMU, coming from unaccounted effects and biases, makes the IMU only solution not so reliable after few minutes. The GPS only solution (SPP) is better in accuracy (note that multi-constellation, multi-frequency and augmentation with PPP, RTK are way more precise) and is noisier. It is also noted that there is a solution outage around 35884 GPS seconds. By combining IMU and GPS, the solution has no outages. However, the solution for LC and TC looks a bit different. As the LC mode rely on the individual solutions of the IMU and GPS that are later combined in the Kalman filter, the absence of GPS solution during satellite outages prevents the update in the filter. During the satellite outages, the IMU only solution starts to drift until the GPS solution is available which re-aligns the IMU. In contrast, the TC algorithm uses only one Kalman filter where the IMU predicted pseudorange and doppler measurements are updated from the GPS measurements of pseudorange and doppler from the available satellites (even 1, 2 or 3 satellites aid in the update stage). This results in robust solution and better accuracy as seen in Figure F1 for the position solution and Figure F2 for the attitude solution.

The trust worthiness of the computed solution is a key in aircraft navigation to fulfil the required navigation performances. It is influenced by the implemented algorithms and from Figure F3, TC solution offers better trust worthiness in the solution as shown by the sdx, sdy, sdz (three components in position) 1-sigma value (dashed line very close to zero). The solid lines for sdx, sdy and sdz (shown in the legend as well) for LC are higher in values. It is also shown that the used number of satellites for TC mode is not zero during the loss of satellites (available satellites below 4) while it is zero for LC mode.

The robustness of the GPS+IMU integration does not only rely on the available satellites and measurements. Albeit not much application for aircraft, the urban navigation regularly faces tough environment that disrupts the quality of the used GPS signals. In addition, the ongoing GPS jamming and spoofing events throughout the world present a complex challenge for GPS+IMU algorithm. The outlier and anomaly detection based on the innovation residuals is a common practice. Figure F 4 and F5 show examples how such events can be detected and excluded in the solution. (Curran et.al, 2017), (Bruggemann et.al, 2011), and (Tanil et.al, 2016) provide various approaches and algorithms for such fault and anomaly detections using the GPS and IMU integration. Even though the data used in the analysis is not directly coming from the aircraft, the concept is analogous and for similar readings (Schmidt et.al, 2010) provides the impact of LC, TC solutions for different scenarios including jamming and fault events for aircraft navigation.

The impact of the fine tuning of the process noise and measurement noise for the used IMU and GNSS system was not analyzed, however, will be targeted in future issues. For understanding the noise characteristics of IMU sensors, (Niu et.al, 2022), (Suvorkin et.al, 2024), and (Kj et.al, 2016) are informative.

Only the GPS system is considered in above analysis and discussion, however, the interoperability of other GNSS enables robust solution. With multiconstellation and multi-frequency, the performance of the GNSS+IMU integration becomes stronger. While the use case in avionics was the focus in this article, the future articles will bring the analysis and discussions in autonomous vehicle, car navigation and robotics together with other sensors like LIDAR and camera that also enable Simultaneous Localization and Mapping (SLAM).

Monthly Performance Remarks:
1. Satellite Clock and Orbit Accuracy:
• The performance of GPS and Galileo are relatively stable and unchanged from previous month. The performance for Beidou, QZSS and GLONASS seemed to have dipped slightly. There were a couple of days with degraded orbits for QZZ. The orbit accuracy statistics Beidou between DOY 17 and 22 degraded by few centimeters. The in-depth analysis of Beidou and QZSS orbit and clock will be performed in future issue to identify any potential faults.
• For Galileo, there was a rare satellite maneuver (E12 from DOY 022). In terms of clock, there was not any large discontinuity for GPS. However, Galileo E29 had a large clock discontinuity on DOY 006.
• For IRNSS, the clock for I06 appeared to be good than previous months. URA value for I09 has higher number of samples for 2.8 m than before.
2. UTC Prediction (GNSS-UTC): All constellations show stable UTC prediction with minor variations. It is one of the best months in last one year.

References

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BIMP (2024 b) https://e-learning. bipm.org/mod/folder/view. php?id=1156&forceview=1

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Niu, Z.; Li, G.; Guo, F.; Shuai, Q.; Zhu, B (2022) An Algorithm to Assist the Robust Filter for Tightly Coupled RTK/IMU Navigation System. Remote Sens. 2022, 14, 2449. https:// doi.org/10.3390/rs14102449

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https://cggtts-analyser.streamlit.app

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

Data sources and Tools:

https://cddis.nasa.gov (Daily BRDC); http://ftp.aiub.unibe.ch/CODE_MGEX/ CODE/ (Precise Products); BKG “SSRC00BKG” stream; IERS C04 ERP files

(The monitoring is based on following signals- GPS: LNAV, GAL: FNAV, BDS: CNAV-1, QZSS:LNAV IRNSS:LNAV GLO:LNAV (FDMA))

Time Transfer Through GNSS Pseudorange Measurements: https://elearning.bipm.org/login/index.php

Allan Tools, https://pypi.org/ project/AllanTools/

gLAB GNSS, https://gage.upc.edu/ en/learning-materials/softwaretools/glab-tool-suite