How does a LEO GNSS constellation evolve and affect PPP convergence?

Why LEO geometry changes PPP convergence

PPP estimates a precise position from undifferenced carrier phase observations, but it needs a long convergence time that depends on atmospheric effects, multipath, satellite geometry, and algorithm design. The paper's premise is that low-orbit satellites move quickly across the sky, so the geometry of the positioning solution changes fast, which the authors expect to accelerate PPP convergence and carrier phase ambiguity resolution relative to medium-earth-orbit GNSS.

The study tests that expectation on Xona's Pulsar constellation, which is designed both to augment GNSS through compatible signals and to operate as an independent system. Pulsar is compared to MEO GNSS in two roles: as an augmentation to GPS, and as a standalone service, using availability, dilution of precision, and PPP convergence as the comparison metrics.

Four deployment stages and what each enables

Pulsar is evaluated at 16, 48, 192, and 258 satellites, all at a nominal altitude of 1080 km in circular orbits. The 16-satellite minimum viable product uses two inclined planes of eight satellites each at 53 degrees inclination, and the paper says this stage offers intermittent visibility in most populated areas, best in mid-latitude bands, suitable for precise time transfer, intermittent positioning including stationary indoor users, and GNSS augmentation.

At 48 satellites, latitudes between roughly plus and minus 20 to 65 degrees have at least one satellite in view at least 99.5% of the time, with longer gaps near the equator and the far north and south. At 192 satellites, the 12 inclined planes are fully populated and at least four Pulsar satellites are visible above a 5-degree elevation mask 99.5% of the time from -70 to +70 degrees latitude, covering all major populated locations. The full 258-satellite constellation adds six polar planes of 11 satellites each at 97.5 degrees inclination, giving global coverage with redundancy.

Availability is not service uptime

The paper defines availability as line-of-sight visibility to a satellite, not service availability. The authors state explicitly that 95% geometric availability does not equate to 95% service uptime once space system reliability, ground system reliability, or environmental factors are accounted for. This distinction matters because the headline coverage numbers describe geometry, not guaranteed service.

The elevation mask also changes the picture. With a 5-degree mask, many mid-latitude locations have at least one Pulsar satellite visible 95% of the time or more at the 16-satellite stage, but raising the mask to 10 degrees drops that availability below 90% globally. The authors note this highlights the challenge LEO constellations face in urban environments, where buildings often mask 30 degrees or higher.

DOP gains saturate as satellites multiply

At 192 satellites, Pulsar offers HDOP close to or less than 1, and the number of satellites in view reaches a maximum of 16 at mid-latitudes. Comparing visibility and HDOP by latitude shows a non-linear relationship: going from about 13 to 16 visible satellites yields only a modest HDOP improvement, while going from around 8 to more than 10 satellites produces a substantially larger HDOP reduction. The paper concludes that the greatest geometric gains come when moving from lower to moderate satellite availability, with diminishing returns as the constellation densifies.

At full operational capability, Pulsar's PDOP falls comfortably below the value of 6 that the paper treats as sufficient geometry for GPS position estimation, at all latitudes. The minimum number of visible satellites anywhere is 6, with some locations having minimums as high as 14, and the maximum at any location exceeds 20. The authors present this as evidence that Pulsar can operate as a standalone PNT constellation independent of other GNSS.

Two PPP tests with different evidence

The PPP analysis uses two methods that answer related but distinct questions. Part 1 is a global software simulation: observations are generated with a 5-degree elevation mask at 1 Hz for 176 static user locations across all latitudes, and the PPP filter is run once per hour for 24 hours for 400 seconds each, producing over 4000 simulated PPP scenarios per constellation combination. GPS + Galileo is the MEO baseline, and the paper compares standalone GPS versus standalone Pulsar and GPS augmented by Pulsar. Because observations are generated in simulation, clock offsets and atmospheric delays are resolved cleanly with minimal impact on position error.

Part 2 processes real data from Pulsar-0, the in-orbit-validation satellite, through a modified RTKLIB implementation. Pulsar-0 orbits at 520 km with a 97-degree polar inclination, and its recorded pass peaked at 68 degrees elevation with a carrier-to-noise density ratio of 57 dB-Hz. Because modelling and estimating satellite clock biases and other errors from a single satellite source is difficult, this part uses covariance analysis rather than position error, deriving precision metrics from the diagonal elements of the EKF covariance matrix rotated into a local east, north, up frame.

Convergence improvement scales with constellation size

In the global simulation, combining GPS with Pulsar improves the float solution convergence time at all four deployment stages: 18.8% with 16 Pulsar satellites and 83.8% with 258 Pulsar satellites. These are simulated position-error results from a simple PPP estimator, and the paper notes that to the authors' knowledge no commercially available positioning engine has implemented PPP with LEO, so the simulation is intended to predict rather than measure live performance.

In the Pulsar-0 covariance analysis, the real-data case shows significantly faster covariance convergence. The paper is careful about what this does and does not show: the covariance matrix is estimated from satellite positions and measurement variances independent of state estimates or observations, so it isolates geometry from observation errors. The authors state that neither case can claim to be fully representative of live PPP performance, but that the simulated position error and the real-data covariance together make a case for future Pulsar PPP performance.

Pulsar-0 ranging precision and its limits

Early on-orbit measurements from Pulsar-0 showed pseudorange residuals with an RMS of 43 mm over the reported test interval, which the paper describes as low short-term code-domain measurement scatter. The authors immediately qualify this: the published analysis does not independently quantify satellite orbit and clock errors relative to defined terrestrial and time references, so the value should not be read as a formally established SISRE or system-level URE. A like-for-like comparison with GPS would require equivalent measurement definitions, reference products, and statistical treatment.

The RTKLIB settings used for the Pulsar-0 case are also described as coming from very early testing. The carrier phase error is increased to 5 cm to give the filter more leniency in accepting observations, pseudorange errors are 100 times larger than carrier phase errors, and the paper states that any positioning engine integrating LEO observations will likely require further filter tuning.

Where Pulsar augmentation pays off first

The paper's own priority ordering is that Pulsar's value as a GPS augmentation arrives earlier than its value as a standalone system. The 18.8% convergence improvement at just 16 satellites means augmentation benefits begin at the minimum viable product stage, before Pulsar can support independent positioning. Standalone capability is tied to later stages: HDOP near or below 1 at 192 satellites, and PDOP below 6 at all latitudes plus a global minimum of 6 visible satellites at 258.

The most decision-relevant threshold in the paper is therefore not the final constellation size but the 16-satellite stage, where augmentation already improves convergence, combined with the 192-satellite stage, where standalone geometry becomes comparable to GPS outside the far north and south. The authors also note that Pulsar's inclined planes give it an advantage over GPS in visibility at mid-latitudes, while GPS retains limited availability at far northern and far southern latitudes.

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