A BDS–eLoran fusion positioning method for resilient PNT under reduced satellite availability

Why backup navigation matters

Modern life quietly depends on satellite navigation. Ships, planes, financial networks and power grids all rely on signals from space to know exactly where—and when—they are. But those signals are weak and can be blocked, jammed or spoofed. This article explores a practical way to add a robust backup on Earth, so that navigation and timing keep working even when satellites falter, especially for ships at sea.

Two very different ways to find your way

Today’s navigation workhorse is the family of satellite systems known collectively as GNSS, which includes GPS and China’s BeiDou (BDS). Receivers calculate their position by timing signals from at least four satellites. If fewer are visible because of interference, equipment failure or geography, the usual method simply breaks down. In contrast, eLoran is a modern version of an older radio navigation network that uses powerful, low‑frequency transmitters on land. Its signals travel along Earth’s surface and are extremely hard to jam, making them a strong candidate for a complementary system rather than a replacement for satellites.

Turning an old radio network into a smart partner

On its own, eLoran is not accurate enough for many modern uses. Its signals are slowed and distorted by the atmosphere, the ground and coastal terrain, which can cause position errors of hundreds of meters. The authors first show how measurements from BeiDou can be used to clean up these distortions at a fixed test site. By comparing the true distance from the receiver to each eLoran station (derived from BeiDou) with the time it takes the eLoran signal to arrive, they estimate the extra delay caused by the environment. These delay corrections are then smoothed with a Kalman filter, turning a noisy long‑wave signal into a much more reliable ranging source.

Blending sky and ground signals in one framework

The heart of the work is a unified positioning method that treats satellite and eLoran measurements together, instead of using eLoran only as a crude backup. The fusion algorithm is designed to keep working as the number of visible satellites drops from four or more down to one. It does this by writing joint equations that relate the receiver’s unknown position and clock time to both sets of signals. A key innovation is a dynamic weighting scheme: each measurement is given more or less influence depending on current satellite geometry and how well the eLoran delay corrections are behaving. When satellite geometry is poor, or eLoran paths look unstable, their weights are reduced automatically, allowing the system to adapt on the fly.

Testing on real ships in busy seas

The researchers tested their approach in the eastern seas off China, where several eLoran stations form a regional network overlapping BeiDou coverage. After correction, eLoran alone achieved horizontal errors of about 19 meters, a vast improvement over its uncorrected performance. The team then examined mixed configurations: one satellite plus three eLoran stations, two satellites plus eLoran, and so on, up to four satellites. As more satellites were available, accuracy steadily improved. Yet even with a single satellite, three eLoran stations and a simple constraint that the receiver lies at sea level, the system achieved roughly 12‑meter horizontal accuracy—where a standard satellite‑only solution would fail outright because there are not enough satellites to solve the equations.

Graceful degradation instead of sudden failure

To mimic real disruptions, the authors deliberately switched satellites on and off during both fixed and moving‑ship trials. They observed that when satellites were lost, errors grew but stayed within tens of meters, rather than diverging catastrophically. Once satellite signals returned, the fusion system quickly locked back in, restoring meter‑level accuracy within about two seconds. In short, by reframing reduced satellite visibility as a manageable change in “how much is observable,” rather than as an immediate failure, the study demonstrates that a smart combination of space‑based and ground‑based radio can keep navigation and timing services running smoothly through problems that would disable conventional GNSS‑only receivers.

Citation: Li, J., Wu, H. A BDS–eLoran fusion positioning method for resilient PNT under reduced satellite availability. Sci Rep 16, 13349 (2026). https://doi.org/10.1038/s41598-026-43921-x

Keywords: resilient navigation, BeiDou, eLoran, GNSS backup, maritime positioning