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Ionospheric and Plasmaspheric Delay Characterization for Lunar Terrestrial GNSS Receivers with Global Core Plasma Model

This paper characterizes ionospheric and plasmaspheric delays for lunar GNSS receivers by utilizing the Global Core Plasma Model and a custom ray-tracing algorithm to quantify delay magnitudes under varying solar and geomagnetic conditions, thereby informing the design of robust lunar positioning and timing algorithms.

Original authors: Keidai Iiyama, Grace Gao

Published 2026-09-16

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CC BY 4.0

Original authors: Keidai Iiyama, Grace Gao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, the Moon has been a place of silence for our global navigation satellites. Systems like GPS and Galileo are designed to beam signals down to Earth, where they reach our phones or car dashboards. But as humanity looks to return to the Moon and build a permanent presence there, engineers have realized that these same satellites can actually be seen from lunar orbit. The signals are incredibly faint, spilling over the edge of the planet like light from a lighthouse seen from a distant ship, but they are strong enough to be caught by sensitive receivers. This opens the door to using Earth's navigation network to guide spacecraft and astronauts on the Moon, a concept that has moved from theory to reality with recent successful tests. However, there is a catch. As these weak signals travel the 401,000 kilometers from Earth to the Moon, they do not travel through a perfect vacuum. They must pass through two vast, invisible layers of charged gas surrounding our planet: the ionosphere, which sits closer to Earth, and the plasmasphere, a much larger, more diffuse region that extends far into space. These layers act like a thick, shifting fog that slows down the radio waves and bends their path, creating errors in the timing and distance calculations that are critical for navigation.

A team of researchers at Stanford University has now mapped out exactly how much these invisible layers distort signals destined for the Moon. They built a detailed computer simulation to track the journey of these faint radio waves as they travel from GPS and Galileo satellites, through the charged gases of Earth's upper atmosphere, and out to receivers in lunar orbit or on the lunar surface. Instead of assuming the signals travel in a straight line, the researchers used a custom algorithm to trace the actual, slightly curved paths the waves take as they are pushed and pulled by the density of electrons in the space around Earth. They tested these paths under a wide variety of conditions, simulating times of high solar activity when the Sun is bombarding Earth with energy, and times of low activity, as well as different levels of magnetic storms. Their goal was to measure the delay caused by this journey, calculating how much extra time the signal takes to arrive compared to if it had traveled through empty space.

The results reveal that the delay is not a fixed number but a variable that depends heavily on the angle at which the signal enters the atmosphere and the current state of space weather. For signals that skim the edge of the atmosphere at low angles, the delay can be massive, stretching the apparent distance to the satellite by more than one hundred meters during periods of intense solar activity. For signals that pass through higher up, the delay is much smaller, often just a meter or two. The researchers found that the bending of the signal path itself adds a small but measurable amount of extra distance, separate from the slowing effect of the charged gas. They also discovered that the strength of the signal plays a crucial role in the overall error. Signals that pass through more atmosphere are delayed more, but they arrive with a stronger, clearer signal that is less affected by electronic noise in the receiver. Conversely, signals that pass through less atmosphere arrive faster but are fainter and more prone to noise. This creates a difficult trade-off for engineers designing lunar navigation systems: they must choose between a signal that is delayed but clear, or one that is fast but noisy.

The study also showed how sensitive these delays are to the Sun and Earth's magnetic field. When solar activity is high, the charged layers around Earth expand and become denser, causing significantly larger delays for all signals. When the Earth's magnetic field is disturbed by storms, the outer boundary of the plasmasphere shrinks, which surprisingly reduces the total delay for some paths because the signal spends less time in the densest part of the gas. The researchers tested two common frequencies used by GPS, finding that the lower frequency signal suffers from a much larger delay but also has much less noise, while the higher frequency signal has a smaller delay but is more vulnerable to noise. By quantifying these effects, the paper provides a clear guide for building robust navigation systems for the Moon. It shows that to achieve precise positioning, future lunar missions will need to account for these atmospheric delays with sophisticated models that can adjust for the changing conditions of space weather, ensuring that the faint whispers of Earth's satellites can be heard clearly across the void.

Technical Summary: Ionospheric and Plasmaspheric Delay Characterization for Lunar Terrestrial GNSS Receivers with Global Core Plasma Model

Problem Statement
Recent advancements have validated the feasibility of using terrestrial Global Navigation Satellite System (GNSS) signals, including weak sidelobe transmissions, for positioning, navigation, and timing (PNT) at the Moon. However, unmodeled ionospheric and plasmaspheric delays remain a significant error source for lunar users. Unlike terrestrial users who experience near-vertical signal paths, lunar receivers encounter signals traversing the ionosphere and plasmasphere horizontally over extended paths. While dual-frequency receivers can mitigate first-order ionospheric effects, they introduce increased receiver noise, which is critical when tracking weak sidelobe signals. Furthermore, standard empirical models (e.g., Klobuchar, NTCM-G) are not directly applicable to lunar geometries. Accurate prediction of these delays requires explicit modeling of electron density in the plasmasphere, a region extending from roughly 1,000 km to beyond 20,000 km altitude, which contributes significantly to Total Electron Content (TEC) along high-altitude or nighttime paths.

Methodology
The authors developed a simulation framework to characterize first-, second-, and third-order group delays, as well as excess path delays caused by ray bending, for GNSS signals received in lunar orbit and at the lunar south pole.

Plasma Modeling: The study employs the Global Core Plasma Model (GCPM), an empirical electron-density model of the inner magnetosphere. GCPM was selected for its ability to incorporate variable geomagnetic (Kp index) and solar activity (R12 index) conditions. The model integrates submodels for the ionosphere, plasmasphere, plasmapause, magnetospheric trough, and polar cap.
Ray-Tracing Algorithm: A custom, computationally efficient ray-tracing algorithm was implemented to iteratively solve for bent signal paths. The method utilizes a shooting approach where the ray path is divided into a plasmasphere section (modeled via differential equations) and a vacuum section (assumed straight beyond a 4 Earth radii cutoff). The algorithm uses the Nelder–Mead optimization method to determine the initial ray direction that minimizes the distance between the propagated ray and the receiver position, avoiding the need for gradient evaluations or repeated electron density calls during optimization.
Delay Calculation: The simulation computes phase and group refractive indices to derive first-, second-, and third-order delays. It explicitly separates the Total Electron Content (TEC) into line-of-sight (LOS) components and bending-induced components ( $\Delta TEC_{bend}$ ). The total group delay is calculated as the sum of LOS group delay, higher-order delays, bending-induced first-order delays, and excess path length due to ray bending.
Simulation Configuration: Simulations were conducted for five Lunar Communications Relay and Navigation Systems (LCRNS) satellites in lunar orbit and a user at the lunar south pole. The study analyzed GPS L1 and Galileo E1 signals under varying solar (R12 = 10 to 200) and geomagnetic (Kp = 1 to 9) conditions. Receiver noise was modeled based on carrier-to-noise ratio (C/N0) and Delay Lock Loop (DLL) thermal noise characteristics.

Key Contributions

Algorithm Development: The paper proposes a low-cost ray-tracing algorithm using the Nelder–Mead method to iteratively determine bent ray paths without requiring gradient evaluations, ensuring convergence of the computed delays.
Comprehensive Delay Characterization: It presents detailed simulations of first-, second-, and third-order ionospheric/plasmaspheric delays and bending delays for both lunar orbit and surface users, a scope not previously covered for terrestrial GNSS signals observed in lunar orbit.
Parametric Analysis: The study quantifies the influence of signal frequency, geomagnetic activity (Kp index), and solar activity (R12 index) on delay magnitudes and receiver noise.

Results

Delay Magnitudes: Mean group delays are typically on the order of 1 meter but can exceed 100 meters for low-altitude ray paths (tangential altitudes < 500 km) during periods of high solar activity. For tangential altitudes below 500 km, the mean first-order group delay reaches up to 50.59 m.
Altitude Dependence: Delays decrease rapidly with altitude; above 10,000 km, mean group delays fall below 0.2 m. Bending delays are generally smaller than first-order terms but can exceed 1 meter for paths with tangential altitudes under 1,000 km. Notably, the extra delay caused by bending often exceeds the actual increase in geometric path length.
Higher-Order Effects: Second- and third-order delays remain negligible, being several orders of magnitude smaller than the first-order contribution.
Geomagnetic Influence: Contrary to some terrestrial expectations, higher Kp indices (indicating stronger geomagnetic activity) result in generally smaller group delays. This is attributed to the erosion of the plasmasphere, where the plasmapause contracts from 4–6 Earth radii (RE) during quiet conditions to 2–3 RE during strong activity, reducing the volume of high electron density.
Solar Activity Influence: Higher R12 indices (solar activity) produce larger group delays due to increased electron density in the ionosphere and plasmasphere. For instance, to keep the 99th-percentile group delay below 5 meters, the required altitude mask increases from ~2,000 km (R12 ≤ 50) to ~10,000 km (R12 = 200).
Frequency Trade-offs: A bias-variance trade-off exists between L1 and L5 signals. L1 signals exhibit smaller group delays (bias) but higher receiver noise (variance), while L5 signals show larger delays but significantly lower thermal noise. For tangential altitudes up to ~5,000 km, L1 achieves a smaller total User Equivalent Range Error (UERE) because the reduction in group delay outweighs the increase in receiver noise. Conversely, L5 becomes advantageous for high-altitude sidelobe paths where group delays are intrinsically small and thermal noise dominates.

Significance
The paper establishes a foundation for designing robust positioning and timing algorithms that utilize terrestrial GNSS signals in cislunar space. By characterizing the magnitude and variability of plasmaspheric propagation effects under varying solar and geomagnetic conditions, the work informs the selection of signal frequencies, the setting of altitude masks to exclude high-delay signals, and the development of mitigation techniques. The findings highlight that accurate delay modeling is essential for minimizing User Equivalent Range Error (UERE) under the low-observability conditions inherent to lunar GNSS navigation. Future work, as noted by the authors, will focus on validating these simulations with upcoming LuGRE measurements and integrating delay estimation directly into navigation filters.

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