Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions
Abstract
:1. Introduction and Motivation
1.1. LEO-PNT versus GNSS
1.2. Sources of Errors in Satellite-Based Positioning
1.3. Paper Goals, Research Questions, and Main Contributions
- We propose a novel IAMM for ionospheric delay compensation at the receiver;
- We validate the IAMM model by comparing it with current state-of-the-art models used today using real observation data from a variety of GNSS reference stations, as well as from Android mobile receivers;
- We discuss the proposed model’s challenges and possible improvements to the LEO-PNT context.
2. Related Work
2.1. Overview of the Ionospheric Delay Concept
2.2. Klobuchar Model
2.3. NeQuick Model
2.4. Neural Network Models
2.5. IRI Model
2.6. IGS Model and Database
- Final GIMs (11 days);
- A predicted solution (available 1–2 days in advance).
2.7. Ionospheric Models for LEO Satellites
2.8. Summary of State-of-the-Art and Our Proposed Model at a Glance
3. Methodology
3.1. Data Sources
3.2. Data Collection
3.3. IAMM Calculation Strategy
4. Results
4.1. TEC Results
4.2. Ionospheric Delay Results
- Method 1: No ionospheric correction;
- Method 2: Klobuchar ionospheric correction;
- Method 3: IRI ionospheric correction;
- Method 4: IAMM ionospheric correction.
4.2.1. Data from Reference Stations—Static Conditions
4.2.2. Data from Android Devices—Dynamic Conditions
4.3. Results Extended to an LEO-PNT System
5. Discussion and Future Works
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Correction Statement
Abbreviations
AWGN | Additive white Gaussian noise |
BDGIM | BeiDou Global Broadcast Ionospheric Delay Correction Model |
CDDIS | Crustal Dynamics Data Information System |
CMEs | Coronal mass ejections |
COSPAR | Committee on Space Research |
DFRs | Dual-frequency receivers |
ED | Electron density |
FFT | Fast Fourier transform |
GEO | Geo-stationary orbit |
GIMs | Global ionospheric maps |
GNSS | Global Navigation Satellite Systems |
GPS | Global Positioning System |
IAMM | Interpolated and Averaged Memory Model |
ID | Ionopsheric delay |
IGS | International GNSS Service |
IONEX | IONosphere map EXchange format |
IoT | Internet of Things |
IRI | International Reference Ionosphere |
ISR | Incoherent scattered radar |
IWG | Ionosphere Working Group |
LEO | Low Earth orbit |
LOS | Line of sight |
MEO | Medium Earth orbit |
ML | Machine learning |
NASA | National Aeronautics and Space Administration |
NLOS | Non-line-of-sight |
NLS | National Land Survey of Finland |
NMEA | National Marine Electronics Association |
NOAA | National Oceanic and Atmospheric Administration |
PNT | Position, Navigation, and Timing |
PPP | Precise point positioning |
QZSS | Quasi-Zenith Satellite System |
Q4DIM | Quasi-4-Dimension Ionospheric Modeling |
RF | Radio frequency |
RIM | Regional ionospheric map |
RINEX | Receiver-independent exchange format |
RMS | Root mean square |
RSS | Received signal strength |
RT-GIMs | Real-time global ionospheric maps |
SLM-MF | Single-layer model mapping function |
SFRs | Single-frequency receivers |
SPP | Single-point positioning |
STEC | Slant total electron content |
TDL | Tapped delay line |
TEC | Total electron content |
TECU | TEC units |
ToA | Time of arrival |
URSI | Union of Radio Science |
VTEC | Vertical total electron content |
WLS | Weighted least squares |
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Ref. | Model | Type | Broadcast | Input Data | Direct Output Data |
---|---|---|---|---|---|
[40] | Klobuchar | Empirical | Yes | Atmospheric coef., approx. receiver position | ID |
[42] | NeQuick | Empirical | Yes | Atmospheric coef., approx. user position | ED, ID |
[31,33,44,45] | Neural networks | Data-driven | No | Data from other models/stations | TEC, ID |
[52] | IRI | Empirical | No | Ionosondes, ISRs, in situ data (satellites) | ED, ID, ionosphere detailed composition (see Section 2.5) |
[53] | IGS (GIMs) | Mathematical | No | Dual-frequency measurements from GNSS stations | IONEX files |
This work | IAMM | Data-driven | No | Approx. receiver position, Y matrix (see Section 3.2) | TEC, ID |
R | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Solar Year | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 1 | 2 | 3 | 4 |
Number of Points Used in Statistics | Correlation Coefficient |
---|---|
5183 | 0.9283 |
15,549 | 0.9574 |
31,098 | 0.9589 |
AVG [m] | No Correction | Klobuchar | IRI | IAMM (Proposed) |
---|---|---|---|---|
Mean | 5.390 | 3.244 | 3.159 | 1.976 |
– | (−39.7%) | (−41.4%) | (−63.3%) | |
StD (1-) | 1.277 | 1.051 | 1.0682 | 0.848 |
– | (−17.7%) | (−16.4%) | (−33.6%) | |
a Using observations from Tampere University (high-grade) | ||||
AVG [m] | No Correction | Klobuchar | IRI | IAMM (Proposed) |
Mean | 6.209 | 4.252 | 4.397 | 4.1708 |
– | (−31.5%) | (−29.2%) | (−32.8%) | |
StD (1-) | 3.470 | 3.219 | 3.141 | 3.164 |
– | (−7.2%) | (−9.5%) | (−8.8%) | |
b Using observations from the FinnRef network (high-grade) | ||||
AVG [m] | No Correction | Klobuchar | IRI | IAMM (Proposed) |
Mean | 42.815 | 34.052 | 38.884 | 36.388 |
– | (−20.5%) | (−9.2%) | (−15%) | |
StD (1-) | 18.710 | 18.103 | 18.397 | 18.211 |
– | (−3.2%) | (−1.7%) | (−2.7%) | |
c Using observations from Android smartphones (low-power) |
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Imad, M.; Grenier, A.; Zhang, X.; Nurmi, J.; Lohan, E.S. Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions. Computers 2024, 13, 4. https://doi.org/10.3390/computers13010004
Imad M, Grenier A, Zhang X, Nurmi J, Lohan ES. Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions. Computers. 2024; 13(1):4. https://doi.org/10.3390/computers13010004
Chicago/Turabian StyleImad, Majed, Antoine Grenier, Xiaolong Zhang, Jari Nurmi, and Elena Simona Lohan. 2024. "Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions" Computers 13, no. 1: 4. https://doi.org/10.3390/computers13010004
APA StyleImad, M., Grenier, A., Zhang, X., Nurmi, J., & Lohan, E. S. (2024). Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions. Computers, 13(1), 4. https://doi.org/10.3390/computers13010004