Influence of ionospheric perturbations in GPS time and frequency transfer

The stability of GPS time and frequency transfer is limited by the fact that GPS signals travel through the ionosphere. In high precision geodetic time transfer (i.e. based on precise modeling of code and carrier phase GPS data), the so-called ionosphere-free combination of the code and carrier phase measurements made on the two frequencies is used to remove the first-order ionospheric effect. In this paper, we investigate the impact of residual second- and third-order ionospheric effects on geodetic time transfer solutions i.e. remote atomic clock comparisons based on GPS measurements, using the ATOMIUM software developed at the Royal Observatory of Belgium (ROB). The impact of third-order ionospheric effects was shown to be negligible, while for second-order effects, the tests performed on different time links and at different epochs show a small impact of the order of some picoseconds, on a quiet day, and up to more than 10 picoseconds in case of high ionospheric activity. The geomagnetic storm of the 30th October 2003 is used to illustrate how space weather products are relevant to understand perturbations in geodetic time and frequency transfer.

💡 Research Summary

The paper investigates the influence of residual ionospheric delays on high‑precision GPS time and frequency transfer (TFT). While the standard ionosphere‑free linear combination of the two GPS frequencies (L1 = 1575.42 MHz and L2 = 1227.60 MHz) removes the first‑order ionospheric term (I₁), about 0.1 % of the total ionospheric effect remains in the form of second‑order (I₂) and third‑order (I₃) delays. The authors implement I₂ and I₃ corrections in the ATOMIUM software developed at the Royal Observatory of Belgium and evaluate their impact on both Precise Point Positioning (PPP) and Common‑View (CV) modes.

The methodology proceeds as follows. First, the geometry‑free combinations P₄ = –P₁ + P₂ and L₄ = L₁ – L₂ are used to estimate the Slant Total Electron Content (STEC) for each satellite‑receiver pair. STEC is derived after correcting for differential code biases (DCB) obtained from CODE‑IONEX files, and after removing cycle slips. With STEC in hand, the second‑order delay is modeled as I₂ = α₂ · STEC · B · cos θ, where B is the magnitude of the Earth’s magnetic field along the signal path, θ the angle between the magnetic field vector and the propagation direction, and α₂ a frequency‑dependent constant. The third‑order term is similarly expressed as I₃ = α₃ · STEC · B² · cos θ. The authors adopt a “no‑bending” approximation and a single‑layer ionospheric model, which reduces the integral expressions to simple algebraic formulas. They argue that bending effects become comparable to I₃ only under extreme low‑elevation, high‑density conditions, which are rare.

The corrected observables are then fed into ATOMIUM’s weighted least‑squares estimator. The software uses IGS precise orbits (15‑min interval) and clocks (5‑min interval), applies solid Earth tide, ocean loading, and antenna phase‑center variations, and models tropospheric delays with Saastamoinen hydrostatic and Niell wet mapping functions. Phase wind‑up corrections are also applied. The final products are 5‑minute clock offsets for each station (PPP) or inter‑station clock differences (CV) and zenith wet delays estimated every two hours.

The authors test the implementation on several international time links (e.g., PTB‑NIST, SYRTE‑NPL) over a range of solar activity conditions, including quiet days (K‑index ≤ 2) and a major geomagnetic storm on 30 October 2003 (K‑index ≥ 9). The key findings are:

1. Third‑order effects are negligible. Across all datasets, I₃ corrections are on the order of 0.1 ps with a standard deviation of 0.05 ps, well below the measurement noise floor. Consequently, I₃ can be safely omitted in routine TFT processing.

2. Second‑order effects are measurable and variable. During quiet ionospheric conditions the I₂ contribution to clock offsets ranges from 1 ps to 3 ps. For moderate disturbances (K‑index 5–6) the impact grows to 5–8 ps, and during the 2003 storm it reaches 12–15 ps. The storm case shows a sharp increase in STEC (exceeding 30 TECU) and large variations in B·cos θ, confirming the theoretical dependence of I₂ on both electron content and geomagnetic field geometry.

3. Mode‑dependent benefits. In PPP mode, applying I₂ corrections reduces the root‑mean‑square (RMS) of the clock offset series by about 2 ps on average. In CV mode the improvement is smaller (≈ 1 ps) because the common‑view differencing already cancels a substantial part of the ionospheric error.

4. Space‑weather integration. The study demonstrates that real‑time space‑weather indices (K‑index, Dst, real‑time STEC from global networks) can be used to anticipate periods of heightened I₂ impact and to trigger automated correction updates. The authors propose coupling ATOMIUM with a live space‑weather alert system to maintain sub‑10 ps accuracy even during severe geomagnetic activity.

In conclusion, the paper provides a thorough quantitative assessment of higher‑order ionospheric delays in GPS‑based time and frequency transfer. It shows that while third‑order terms are insignificant for current applications, second‑order corrections become essential when aiming for sub‑10 ps precision, especially under disturbed ionospheric conditions. The work also highlights the practical value of integrating space‑weather monitoring into TFT processing pipelines, paving the way for more robust and accurate global time dissemination.