In-orbit Demonstration of X-ray Pulsar Navigation with NinjaSat

Abstract: This study demonstrated the pulsar navigation capability of the CubeSat X-ray observatory NinjaSat, which is equipped with two Gas Multiplier Counters (GMCs). The GMCs are sensitive to the 2-50 keV energy band and have an effective area of 16 cm^2 per module at 6 keV. We verified the timing accuracy by observing the Crab Pulsar and confirmed stable timing performance within 100 microseconds. To demonstrate pulsar navigation, we applied a method that optimizes orbital parameters to maximize the significance of the pulsar X-ray pulse profile, known as the Significance Enhancement of Pulse-profile with Orbit-dynamics (SEPO) method. We observed the Crab Pulsar with a total exposure of approximately 100 ks at different epochs and analyzed the data transmitted to the ground. By comparing the optimized orbit with the satellite position derived from Global Positioning System data, we quantitatively evaluated the navigation performance. The results show that the position component along the Crab line of sight was consistently constrained within approximately 40 km, and the three-dimensional position error ranged from 27 to 370 km depending on the observation epoch. These results demonstrate the feasibility of applying a CubeSat-class X-ray observatory to pulsar navigation and provide the first experimental verification that the accuracy of the SEPO method depends on the seasonal geometry between the orbital plane and the pulsar direction.

• The paper demonstrates single-pulsar navigation with NinjaSat’s compact X-ray detectors, achieving stable absolute timing with an 8 ± 1 μs mean offset relative to NICER.
• The SEPO Bayesian optimization method constrained position along the Crab Pulsar’s line of sight to within about 40 km, while three-dimensional errors ranged from 27 to 370 km depending on orbital geometry.
• The results show that seasonal pulsar–orbit geometry controls navigation stability and that pulsar measurements can outperform stale TLE predictions, although onboard processing and GPS-independent timing remain future challenges.

This paper reports an in-orbit demonstration of X-ray pulsar navigation using NinjaSat, a 6U CubeSat X-ray observatory in a 530 km sun-synchronous polar orbit (SSO). The work extends pulsar-based navigation—previously demonstrated on large platforms such as Insight-HXMT and NICER/SEXTANT—to a compact, low-power platform: two Gas Multiplier Counter (GMC) modules, each 1 U in size, 1.2 kg, and consuming at most 2.0 W, sensitive to 2–50 keV with an effective area of 16 cm² per module at 6 keV (2602.14166). Because small instruments have limited effective area and can observe only a restricted set of pulsars, the study adopts the SEPO method ("Significance Enhancement of Pulse-profile with Orbit-dynamics"), which requires only a single pulsar.

Timing system and calibration

Each GMC records photons event-by-event with an FPGA real-time counter at ~61 μs resolution; absolute time is reconstructed on the ground by linearly interpolating between GPS pulse-per-second latches appended to the data stream. Absolute timing was verified against the Jodrell Bank Observatory (JBO) radio ephemeris of the Crab Pulsar by fitting Nelson's formula to the folded main peak across observations from February 2024 to April 2025. The X-ray primary peak leads the radio reference by $(-5.1 \pm 0.4)\times10^2$ μs, consistent with the known radio–X-ray offset confirmed independently by XRISM and NICER absolute timing studies; the epoch-to-epoch scatter is only ~20 μs, i.e., timing performance is stable well within 100 μs.

A more stringent check used simultaneous Crab observations with NICER in the 2–12 keV band, cross-correlating folded pulse profiles at six epochs between 2024 and 2025. Individual offsets ranged from −15 to +38 μs, with a weighted mean of $8 \pm 1$ μs and a standard deviation of 21 μs. This establishes that a CubeSat-class gas detector with GPS-disciplined timekeeping achieves timing fidelity comparable to flagship timing missions, which is the prerequisite for any pulsar navigation application.

Navigation method

The SEPO formulation treats orbit determination as a search for orbital parameters that maximize the $\chi^2$ sharpness of the epoch-folded pulse profile when photon arrival times are barycentrically corrected with candidate orbits. Whereas prior demonstrations varied parameters individually, this work performs simultaneous Bayesian optimization over five SGP4 inputs—the drag term $B$, inclination $i$, mean motion $n$, initial orbital phase $\theta$, and ascending node $\Omega$—assuming a circular orbit ($e = \omega = 0$), justified by NinjaSat's eccentricity below 0.001. Optimization uses GPyOpt with a Matern52 Gaussian-process kernel and lower-confidence-bound acquisition, terminated at 1000 iterations because computational cost grows nonlinearly beyond that point. Search ranges were set an order of magnitude wider than those used for Insight-HXMT and POLAR (e.g., ±5° in $i$, ±10° in $8 \pm 1$0 and $8 \pm 1$1), reflecting the greater orbital variability expected for a small satellite.

Four long-term Crab observations (~80–130 ks exposure each) were selected at epochs spanning different seasonal geometries between the orbital plane normal and the Crab direction: April 2024 (29–30° separation), November 2024 (138–149°), January 2025 (68–74°), and February 2025 (43–50°).

Navigation results

Comparing SEPO-derived orbits against GPS-derived positions in ECEF coordinates yields strongly epoch-dependent accuracy:

Epoch	Euclidean norm RMS (km)	Along-Crab RMS (km)
Apr 2024	370	34
Nov 2024	27	13
Jan 2025	49	18
Feb 2025	53	27

The position component along the Crab line of sight is consistently constrained within ~40 km at all epochs, whereas the full three-dimensional error varies from 27 km to 370 km depending on geometry. Notably, unlike NORAD TLE-derived orbits—which degrade to tens-of-kilometer errors within roughly one week—the SEPO solution remains stable over the observation span, and at ~300–400 ks into the November 2024 and February 2025 runs the pulsar-derived position surpassed the TLE-based estimate. This supports the use of pulsar observations for semi-autonomous orbital updates when TLE or GPS information becomes stale or unavailable.

The paper also provides the first experimental verification that SEPO accuracy depends on seasonal orbital–pulsar geometry. When the pulsar lies nearly perpendicular to the orbital plane (April 2024), variations in $8 \pm 1$2 produce little line-of-sight motion and short-term orbital phase cannot be constrained, producing a strong $8 \pm 1$3–$8 \pm 1$4 degeneracy and unstable optimization. When the pulsar is nearly parallel to the plane normal (January 2025), $8 \pm 1$5 is tightly constrained but $8 \pm 1$6 and $8 \pm 1$7 become poorly determined, yielding apparently good but non-robust solutions. Intermediate geometries (~45°, November 2024 and February 2025) project all orbital elements onto the line of sight and give the most stable convergence. This implies that pulsar selection should be adapted to the orbital configuration and observation season.

Limitations and open questions

The authors identify several caveats. First, the achieved along-pulsar accuracy (tens of kilometers) exceeds the statistical floor predicted by the Sheikh et al. relation—using measured SNRs of ~140–160 and a Crab pulse width of 1.2 ms gives $8 \pm 1$8–1.3 km—by more than an order of magnitude. The excess is attributed to timing measurement uncertainties, residual Bayesian optimization error (position differences of 6–41 km persist even among samples whose $8 \pm 1$9 varies by less than 0.5%), and data gaps from auroral-belt passages, South Atlantic Anomaly transits, and Earth occultation, which leave only partial orbit segments constraining the fit. Which orbital elements drive the fluctuations seen in the regret curves for April 2024 and January 2025 remains unresolved. Second, all results are ground-processed demonstrations validated against GPS; onboard implementation was not attempted. Third, the clock was calibrated with GPS signals, so deep-space applicability would require alternative timekeeping such as onboard atomic clocks. Finally, extending navigation beyond a single bright pulsar will require improved detector sensitivity and corrections for binary orbital motion and accretion-driven spin variations of candidate pulsars.

Conclusion

NinjaSat demonstrates that a CubeSat-class X-ray observatory—with two 1 U, 2 W gas detectors totaling 32 cm² effective area—can achieve sub-100 μs stable absolute timing (8 ± 1 μs mean offset relative to NICER) and perform single-pulsar navigation via Bayesian SEPO, constraining position along the pulsar line of sight to within ~40 km and three-dimensional position to 27–370 km depending on orbital–pulsar geometry. The demonstration establishes CubeSats as viable platforms for pulsar navigation experiments and empirically confirms the geometric dependence of SEPO accuracy, while leaving open the reduction of systematic errors toward the kilometer-level statistical limit and the removal of the GPS dependence for deep-space operation.