The challenge is fundamental rather than incremental. Existing autonomous navigation techniques each carry trade-offs that make them ill-suited to the combined demands of all-weather operation, high accuracy, and long endurance. Visual navigation falters in cloud, darkness, or featureless terrain. Terrain matching requires accurate reference maps and relatively low flight profiles. Inertial navigation systems drift: small errors in measured acceleration accumulate relentlessly into position errors that grow to kilometers within minutes for high-speed flight. Celestial navigation offers global availability but modest precision, while geomagnetic navigation suffers from the irregularity and slow variation of the Earth’s magnetic anomalies. No single method, and no simple combination of them, has satisfied the stringent requirements of long-duration, high-precision flight through environments where external signals cannot be trusted.

The Beihang team’s insight was to extend a principle proven in spacecraft formation flying to vehicles that operate within the atmosphere at altitudes of tens to hundreds of kilometers. In orbital formations, the relative position vectors between spacecraft encode information about the gravitational field, and because gravity depends on absolute position, those vectors can be inverted to determine where the vehicles actually are. The complication for atmospheric flight is that high-altitude high-speed vehicles are subject to large non-conservative forces—engine thrust and aerodynamic drag and lift chief among them—which contaminate the dynamical picture. Gravity is a conservative force, but thrust and aerodynamic forces are not, and unless their contribution can be removed, the gravitational signature hidden in the relative motion is masked.

The researchers’ solution is elegant in its use of existing onboard hardware. Each vehicle measures the non-conservative accelerations directly with the accelerometers of its inertial navigation system. Meanwhile, the relative position vectors between vehicles in the formation are obtained through laser ranging, which supplies highly accurate separation distances, combined with optical direction finding, which supplies the line-of-sight direction. Star trackers, which determine attitude by observing fixed stars, complete the sensor suite by anchoring the measurements in a known reference frame. These three data streams are fused in an extended Kalman filter that outputs continuous estimates of position, velocity, and accelerometer biases. The computational heart of the method lies in differentiating the relative position vectors to derive relative acceleration, subtracting the measured non-conservative accelerations, and thereby extracting the residual gravitational acceleration—the quantity that reflects absolute position—from which the vehicles’ locations are iteratively solved.

To make the scheme rigorous, the team formulated the system in the Earth-Centered Earth-Fixed (ECEF) frame, with a state vector comprising position errors, velocity errors, and accelerometer biases. The measurement model uses the relative position vector errors between vehicles, and the extended Kalman filter incorporates the Earth’s rotation and a high-order gravitational field model. A crucial theoretical question was whether the system is observable at all—whether the measurements contain enough information, in principle, to determine the states uniquely. The researchers answered this by constructing the observability matrix from the system output and its time derivatives, then analyzing its rank and condition number through singular value decomposition. Under a central gravitational field assumption, the minimum singular value was on the order of 10⁻⁷ and the condition number approximately 10⁷, indicating good observability; adopting the high-order gravitational field further improved the picture.

The simulation campaign that followed gives the method its most persuasive numbers. In the baseline scenario, a two-vehicle formation flies at an altitude of 50 kilometers and a velocity of 2.0 kilometers per second, separated by 400 kilometers, over a 150-minute mission. Relative position vector measurements are sampled at 1 Hz with a range error of 1 meter and a direction error of 3 arcseconds; star tracker three-axis errors are 3, 3, and 10 arcseconds; the accelerometer bias is 30 μg with random walk noise of 10 μg/√Hz; and initial position and velocity errors are 200 meters and 1 meter per second. Under these conditions, the navigation solution converges within the first hour, with the three-dimensional positioning error stabilizing below 200 meters. Over the final hours of flight, the root-mean-square errors along the three axes reach 127.5, 90.4, and 82.6 meters respectively—a total three-dimensional error of 176.8 meters sustained across a two-and-a-half-hour autonomous mission.

The comparison case makes the significance of that figure vivid. Under identical conditions but relying solely on inertial navigation and star trackers—without the relative position vector measurements—the position error diverges to the order of several kilometers within just 10 minutes. For long-endurance flight, this divergence is fatal: no amount of filter tuning can rescue an inertial solution that has drifted kilometers off course. The relative position vectors act as a continuous gravitational anchor, indirectly sensing the Earth’s gravitational field through differential measurements and thereby eliminating drift without any external reference signal whatsoever. It is this drift-free quality, achieved with sensors already standard on high-end vehicles, that gives the approach its practical appeal.

Just as valuable for engineers is the team’s systematic analysis of which error sources matter most. Accelerometer measurement noise emerged as the dominant factor: raising the noise from 10 μg/√Hz to 30 μg/√Hz grew the three-dimensional error from 177 meters to 317 meters. Formation geometry also plays a meaningful role. Larger spacing between vehicles improves performance, with errors of 237 meters at 200-kilometer spacing falling to 146 meters at 800-kilometer spacing—intuitively sensible, since a longer baseline sharpens the sensitivity of the relative measurements to the gravitational field’s spatial variation. Increased errors in the relative position vector direction and in star tracker attitude both degrade accuracy, as expected. Interestingly, flight altitude between 50 and 200 kilometers has only a minor effect on navigation precision, suggesting the method is robust across a broad operating envelope rather than tuned to a single flight regime.

The implications reach well beyond the simulation. Vehicle formations flying cooperative missions—whether for distributed sensing, coordinated strike, or mutual support in denied airspace—already possess, or could readily incorporate, the laser ranging, optical direction finding, star tracker, and inertial instrumentation the method requires. The navigation solution demands no emissions toward satellites, no reliance on potentially compromised ground stations, and no external signals of any kind, which strengthens survivability and mission assurance in exactly the complex adversarial scenarios that motivate the technology. Because the gravitational information is extracted from inter-vehicle geometry, adding vehicles to a formation could in principle enrich the measurement set further, an avenue the framework naturally accommodates.

The Beihang team is careful to frame the work as a feasible technical solution rather than a finished flight system, and real-world validation will need to confront effects that idealized simulations simplify—dynamic vehicle interactions, real sensor imperfections, and atmospheric variability among them. Yet the core result stands: relative position vectors, a concept proven among spacecraft, can be transferred to vehicles that fight thrust and aerodynamic forces every second of flight, provided the non-conservative accelerations are measured and subtracted with care. With positioning accuracy better than 200 meters over 150 minutes in GNSS-denied conditions, the method transforms a constellation of cooperating vehicles into its own navigation infrastructure—a self-contained map drawn from gravity, starlight, and the geometry of the formation itself.

Subject of Research: Autonomous navigation of high-altitude high-speed vehicles using inter-vehicle relative position vector measurements in GNSS-denied environments

Article Title: Absolute navigation of high-altitude and high-speed vehicles using relative position vector measurements

Article References: Absolute navigation of high-altitude and high-speed vehicles using relative position vector measurements. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: autonomous navigation, GNSS-denied environments, high-altitude high-speed vehicles, relative position vectors, spacecraft formation flying, inertial navigation, star trackers, extended Kalman filter, gravitational field, observability analysis, vehicle formations, Beihang University

Coronal mass ejections, or CMEs, are enormous clouds of magnetized plasma expelled from the Sun during violent eruptions. When directed toward Earth, they can trigger geomagnetic storms capable of disrupting satellites, radio communications, navigation systems and electrical grids. The most powerful events can induce currents in long-distance power infrastructure and interfere with spacecraft operations. Yet predicting exactly when a CME will arrive remains difficult because conventional solar observatories often lose sight of the eruption while it is still far from Earth.

PUNCH is designed to close that observational gap. Its four small spacecraft, launched on March 11, 2025, operate together as a single distributed observatory spanning roughly 8,000 miles. Three spacecraft carry SwRI-developed Wide Field Imagers, while the fourth carries a narrower-field instrument focused closer to the Sun. Working in coordination, the spacecraft observe the solar corona and the emerging solar wind as one connected system rather than treating the Sun’s outer atmosphere and interplanetary space as separate regions.

“Forecasting exactly when a CME will arrive is difficult because many conventional solar cameras often lose sight of the cloud long before it reaches us,” said Craig DeForest, a SwRI scientist, PUNCH principal investigator and lead author of the study. “The SwRI-developed and -led Wide Field Imagers aboard three of the four PUNCH spacecraft are collecting high-resolution images of entire CMEs over most of their trajectory, in greater detail than previously possible.”

The mission’s first fast, Earth-directed CME arrived in late May 2026, providing an important test of PUNCH’s capabilities. The eruption was tracked across approximately nine-tenths of the distance between the Sun and Earth. Rather than relying solely on measurements taken near the Sun and extrapolating the CME’s later motion, researchers followed the expanding front directly through a large portion of interplanetary space. That continuous view gave them information about the eruption’s changing size, direction and speed as it traveled.

To demonstrate the forecasting potential, the scientists used a deliberately simple geometric representation known as the “ice cream cone model.” In this model, the tip of the cone indicates the region on the Sun where the CME originated, while the broad, rounded top represents the expanding cloud of plasma. Although real CMEs can have complex structures and irregular magnetic fields, the simplified model captures essential characteristics of the eruption’s outward motion and expansion.

Researchers manually traced the bright outer edge of the CME in successive PUNCH images collected during May. They then adjusted only three primary geometric parameters to determine how the cloud evolved over time and where its leading edge would intersect Earth’s orbital position. The resulting forecasts, produced retrospectively after the event, identified the CME’s arrival within a 30-minute interval eight hours before the impact. That level of precision is roughly ten times better than the performance currently associated with many forecasting approaches based primarily on coronagraph observations near the Sun.

The result is especially significant because the researchers did not use an elaborate numerical simulation of the solar wind or a detailed reconstruction of the CME’s magnetic structure. Instead, they applied a basic model to unusually comprehensive observations. As additional PUNCH images became available, the predicted arrival time converged and became more stable. The study therefore suggests that better data coverage may be at least as important as greater model complexity when scientists are trying to determine when a solar storm will reach Earth.

The approach could eventually improve warnings for satellite operators, aviation networks, communications providers and electric utilities. A more reliable estimate of a CME’s arrival time would give organizations additional opportunity to place spacecraft in safe operating modes, adjust satellite operations, protect vulnerable electrical equipment and prepare for disruptions to high-frequency radio and navigation signals. Forecasting the direction and strength of an impact remains a separate challenge, however, because the magnetic orientation of a CME strongly influences how severely it interacts with Earth’s magnetosphere.

PUNCH’s broader scientific purpose is to understand how the corona transitions into the solar wind, the continuous stream of charged particles flowing outward from the Sun. By observing that transition and following large-scale structures through the heliosphere, the mission provides a wide-angle view of the environment surrounding Earth. The new study indicates that this perspective may also have immediate practical value. What began as a mission designed to investigate fundamental solar physics could become an important component of future space weather forecasting, turning distant images of solar eruptions into actionable warnings before they reach our planet.

Subject of Research: Improving coronal mass ejection arrival-time forecasting through wide-field space-based imaging.

Article Title: PUNCH Mission Demonstrates More Precise Forecasting of Coronal Mass Ejection Arrivals

News Publication Date: August 4, 2026

Web References: https://www.swri.org/markets/earth-space/space-research-technology/space-science/heliophysics ; https://youtu.be/Qqtakkfo-mg

Image Credits: Southwest Research Institute

Keywords

PUNCH mission, NASA, Southwest Research Institute, coronal mass ejections, CME forecasting, space weather, solar storms, heliosphere, solar wind, geomagnetic storms, satellite protection, Sun-Earth system