Evidence-Supported ASO Catalog

1Summary

Space Data Network (SDN) builds a catalog of anthropogenic space objects (ASOs) from public and login-only sources. Object by object, it publishes the solution with the best measured accuracy for the intended use, with its uncertainty. Accuracy is measured against independent precise orbits, under plans fixed before the test data were read¹. Section 2 states the method step by step, with the rule that gives every object a covariance.

For most objects the only public input is the OMM, and the catalog takes it as it is. What the catalog adds is a measured account of each input's error, and screening that acts on it safely:

1. Measured error as covariance. An orbit propagated from an OMM's epoch state carries a covariance equal to the error measured for its orbit regime and element-set age. That error is measured against independent orbits in every regime that has them: GNSS analysis-centre orbits, laser ranging, LEO precise orbits, operator ephemerides and radio-occultation receivers. A covariance is labeled calibrated only where held-out data confirm it (section 2.2).
2. SDN's own atmosphere. Drag uses JB2008 or NRLMSISE-00 with an open correction in the form of the Space Force's Dynamic Calibration of the Atmosphere, solved from public operator states. It explains 25–40 % of the density variation measured by satellites that did not calibrate it; 1–3-day position error is unchanged (ratios 0.98–1.02) (section 5.4).
3. Maneuvers. A detector reads each object's element-set history for steps in orbital energy and plane, and reports each maneuver's time and size. On held-out data it found 22 of 25 ISS burns and all 6 GPS maneuvers in precise orbits; geostationary station-keeping is harder, 4 of 11 (section 5.5).
4. Better start states where data allow. HPOP's force models agree with Orekit within 1 cm over a day (steps of at most 30 s; 2.5 cm at 300 s, section 7). Fitted to laser ranges, HPOP stays 20–60 times better than SGP4 to 7 days; fitted to an arc of corrected OMMs, it halves SGP4's error to two days in GPS (section 5.3). SGP4-XP sets that SDN fits to precise GNSS orbits err by a median 0.42 km over the seventh day, against 14 km for its SGP4 fits of the same orbits (exploratory, section 4).
5. Screening that stays safe when the covariance is large. A large covariance spreads a collision's probability thin: on real OMM errors, a probability threshold of 1e-4 missed 2.7–16 % of true collisions. Where held-out data confirm the covariance, screening on the uncertainty region missed 0–0.4 %, at the cost of more false alerts, and every event also carries the covariance-free maximum probability⁵⁰. Large uncertainty makes the screen cautious, not blind.

Three results go beyond published work:

1. An element-set correction learned on a LEO fleet carries to that fleet's unseen satellites (25 % lower error at epoch) but not to other operators' satellites, nor across GPS orbital planes; in GNSS a per-satellite bias holds 37 % of the along-track variance, against 1–5 % in LEO (section 5.3).
2. A density correction of the kind the Space Force's drag model uses, solved from Planet's public states, is scored on satellites that did not calibrate it (section 5.4).
3. Consecutive OMM errors are strongly correlated, and four published covariance constructions are overconfident (section 6).

Pre-registered hypotheses that failed are reported as not supported.

2Method

The catalog is assembled object by object from the products of every source. Each object ends with a state, a covariance and its maneuvers.

2.1Construction

1. Read each source at its level. Each record becomes the Space Data Standards (SDS) record of its kind, under the source's own identifier: element sets as OMMs, ephemerides as OEMs, laser normal points and other measurements as observations (sections 3 and 4).

2. Derive the same products from every source. For every object a source covers, the method derives four records:

   1. An SGP4 element set (OMM): the source's own, or one fitted to the source's ephemeris (section 4).
   2. An SGP4-XP element set: an OMM in the extended-perturbation theory of the Space Force's Astrodynamics Standards⁵², with its ballistic and radiation coefficients, fitted to the same data (section 4).
   3. A state with its covariance (OCM): the source's state at its epoch, or the SGP4 epoch state of the handoff in section 4, with the covariance of section 2.2.
   4. The maneuvers in the source's history (MNV), from the detector of section 5.5.

   Sources are then compared like for like, and each can be propagated and shown on its own.

3. Measure each source. Each product is scored against independent precise orbits by object class, orbit regime and product age, under a plan fixed before its test data were read (sections 5 and 10). A source's measured errors form its error model.

4. Associate. Crosswalks propose links between records of one object; ephemerides compared over shared intervals accept, reject or hold each link (section 8).

5. Select. For each object, regime and horizon, the catalog takes the product of the source with the lowest measured median error on a training window of at least 30 samples. Fusing sources was never better than selecting one (section 8).

6. Attach covariance and maneuvers. The selected product keeps its covariance and label (section 2.2). The object carries the maneuvers of all its sources, merged by time and size. A product whose epoch precedes a maneuver does not describe the orbit after it, so selection after a maneuver draws only on later products.

7. Write the catalog. A catalog record (CAT) per object, with its selected OMM, SGP4-XP OMM and OCM and its merged MNV records, each naming the source it came from.

2.2Covariance for every object

Every object carries a covariance, from the first rule that applies:

1. The operator supplies one. The operator's covariance, as supplied.
2. An orbit fit made the product. The fit's formal covariance, scaled by the realism factor measured for that source and object class on held-out data. Unscaled, laser-range fits are 16–21 times too small in mean d²/3 (section 6).
3. The source has an error model for the object's regime. The source's measured error at the element set's age, mapped from radial, in-track and cross-track axes to Cartesian. The model is built from the errors of consecutive element sets against independent precise orbits, with their correlation, and calibrated by regime and age (section 6). AOE's sets match Space-Track's error at equal age (section 4) and take its model.
4. Otherwise. The same model pooled over all sources in the object's regime.

Rules 3 and 4 cover every object with an element set, so no object goes without a covariance.

Each covariance carries a label: the rule, the source, the regime and age cell, and the verdict of held-out data for that cell. Calibrated means the realism rule of section 6 held on held-out data: mean d²/3 in [0.8, 1.25] and 95 % coverage in [0.93, 0.97]. Otherwise the label records the measured mean d²/3 and coverage. The element-set model is calibrated in 2 of 35 regime-and-age cells, LEO above 800 km at issue and at half a day; the HPOP epoch state with per-regime P₀ and Q in 5 (section 6). Screening on the uncertainty region relies on calibrated cells, and every screening event also carries the covariance-free maximum probability, which needs no covariance⁵⁰.

Covariance propagates through HPOP's state-transition matrix with per-regime process noise, or grows with element-set age in the model of rule 3 (section 6).

An orbit solution is an inference with five contributors:

1. The object's physics
2. The dynamics model
3. The observations
4. The measurement model
5. The inference method

A provider's ephemeris or element set already embeds the provider's models and inference, so the catalog treats it as the provider's estimate, not as an observation. Agreement between two products counts as independent confirmation only when their inputs are independent.

Orbit data sit at four processing levels, by analogy with Earth-science data levels. A higher level is more processed, not better: it inherits every flaw below it, and re-epoching adds no evidence. Each input is placed at its level.

A solution states what produced it:

Physical validity rests on the measurements of sections 5 to 7.

3Sources

The inventory² lists 97 public and login-only sources in eight groups, with access, terms, latency and use. Results draw on every source an experiment read; files are copied only where their terms allow, and the credits close this paper.

SpaceMapper's AOE catalog holds SGP4 element sets from its own ground and space sensors (channel KY, 19,202 objects on 11 October 2026) beside sets it relays from other catalogs⁴. AOE rewrites them every 3 hours; SDN reads them daily from the public web pages (section 4). SpaceMapper states no license, so the sets are cited, not copied. Doppler read from SatNOGS waterfall images made the ISS orbit 2.7–10.7 times worse than SGP4 E6.

4Normalization and model dispatch

Vimpel's HEO product gives osculating elements in J2000⁵. The standard perifocal rotation turns them into a J2000 state at the same epoch⁶, with μ = 398,600.4418 km³/s². Vimpel's datefirst file maps its own object numbers to NORAD numbers, with the date each catalog first detected the object; each pair is a candidate link, accepted when the two orbits agree (section 8). An object the file does not map keeps the identifier vimpel:<id>, and no NORAD number is invented⁷. Velocity differenced from 600 s position samples departs from the analytic velocity by up to 1.1 km/s, so it serves only as a diagnostic.

AOE element sets

AOE's KY sets are SGP4 mean elements: the catalog evaluates them through the same SGP4 as Space-Track's OMMs, under the NORAD number AOE gives, or under aoe:<id> where it gives none. E15 scores them against independent orbits beside Space-Track's, under a plan fixed before its test window E15. On 11 October 2026, its first training day:

AOE's sets are therefore not copies of Space-Track's: they are as accurate at the same age, and older on most objects.

An OMM holds SGP4 mean elements, not osculating ones. The catalog evaluates SGP4 at zero elapsed time, transforms position and velocity from TEME to GCRF at the same instant, and starts HPOP from that state⁸. SGP4's drag term B* becomes the ballistic parameter

with ρ₀ from Spacetrack Report No. 3⁹; 0.01 m²/kg stands in where B* ≤ 0, and Cr·A/m is 0.02 m²/kg¹⁰. The handoff is valid; whether it helps is measured in section 5.3.

OMM fields mix nominal (catalog number), ordinal (element-set number), interval (epoch), ratio (mean motion) and circular (node, perigee, mean anomaly) scales, so the pipeline computes on SGP4-evaluated states, never on raw fields. The legacy two-line format quantizes angles to 0.0001°, about 12 m along track near 6,900 km: a resolution, not an accuracy.

Dispatch, frames and time

Each record is routed by its declared theory: mean elements to SGP4, osculating elements to the two-body conversion, states and ephemerides to frame transforms. Osculating elements offered to SGP4 are refused as a model mismatch. Frames follow the IERS Conventions (2010): IAU 2006/2000A, CIO-based, through ERFA, with IERS Earth orientation¹¹. TEME, EME2000, GCRF and ITRF stay distinct; epochs are UTC and integration runs on TT.

SDN fits its own OMMs to any source's ephemeris: operator ephemerides (SpaceX's MEME files, CCSDS OEM, Earth-fixed files), GNSS orbits (SP3), laser-ranging predictions (CPF) and its own HPOP solutions. Each fit gives two element sets over a declared interval, each scored on a held-out stretch before release: an SGP4 set with B*, which any SGP4 implementation reads, and an SGP4-XP set with its ballistic (BTERM) and radiation (AGOM) coefficients, propagated by the Astrodynamics Standards library⁵². CelesTrak's supplemental GP fits operator ephemerides with SGP4 the same way⁴⁸, Spacebook fits extended-perturbation element sets to its own orbits⁵¹, and the 18th Space Defense Squadron's eGP fits SP states⁴⁹. The fit RMS that CelesTrak publishes for each set is the benchmark.

Exploratory, on 24-hour fits to the same states XP: the median root-mean-square 3D position error (km) over the fit and over each later day, SGP4-XP / SGP4.

Starlink files span 2–3 days and the low laser-ranged arcs 4 days, which bounds their horizons. SGP4-XP converged on all 505 windows and SGP4 on 98 of the 120 GNSS windows; the GNSS row compares those 98. Where drag is weak the extended theory holds: 12 to 34 times closer at 7 days on GNSS, LAGEOS and Etalon. On the ISS, where drag and reboosts dominate, the two theories are equal.

5Products by object class

Each row is one method: its originators, our measured result (median 3D position error unless stated) and the experiment. Every experiment froze its plan before reading its test window¹.

5.3Objects with public OMMs only

The start state sets the limit. Over 6 days, HPOP leaves 0.2 km along track from a GPS satellite's IGS state and 8.4 km from its OMM epoch state (medians of 508 arcs)¹⁰. Laser ranges fix the start state, and the prediction then stays 20 to 60 times better than SGP4 to 7 days E6.

Density is scored by σ, the spread of ln(observed/model density) on satellites outside the calibration; prediction by the 3-day position error relative to JB2008's (below 1 is better).

An open, DCA-form correction from public operator states E13. HASDM's Dynamic Calibration of the Atmosphere (DCA) corrects exospheric temperature every 3 hours from the drag of about 75–100 tracked calibration satellites, each with a constrained ballistic-coefficient correction²¹. E13 solves that form from public data alone: the common mode s of the daily drag of 36 Planet Doves, read through orbital energy, corrects JB2008's temperature, with a ballistic coefficient held constant per satellite over a block and a forecast with a 48-hour time constant. Published work derives density from operator ephemerides and scores density alone^26,27,28, or assimilates commercial GPS states²⁹. E13 scores the correction on satellites that did not calibrate it, over ten months of Planet states against Swarm and GRACE-FO, with the storm of January 2026 in a held-out block. With x′ the logarithmic residual of observed against JB2008 density in a 12-hour window,

The correction does not follow storms. Exploratory, on one NRLMSISE-00 reference for every split: the fleet explains 0.47–0.48 of NRLMSISE-00's larger spread, leaving residuals of 0.075–0.095 against 0.069–0.086 on JB2008.

The detector compares the trajectories of consecutive element sets at one instant, whatever propagator answers its queries: a crossing test and a robust likelihood-ratio test for steps in orbit-averaged energy and orbit plane, merged by default¹⁰. It builds on element-set time series³⁰ and the generalized likelihood ratio for jumps³¹. Thresholds came from the ISS in 2020–2024; every other window was read once. A planned ISS burn counts as truth only when NASA's next trajectory shows it executed; one 2021 plan was not.

Covariance propagates through HPOP's state-transition matrix Φ with a declared white-acceleration process noise Q¹⁰:

Φ supplies neither P₀ nor Q; they come from a fit, a provider or an empirical model. Realism is scored against independent precise orbits by $d^2 = \mathbf{e}^{\mathsf{T}} P^{-1} \mathbf{e}$ for a position error e, against χ² with 3 degrees of freedom: a covariance is realistic when the mean of d²/3 lies in [0.8, 1.25] and its 95 % coverage in [0.93, 0.97], the rule of E14 after Zaidi and Hejduk³².

On the held-out window, maneuvers, the storm of 4 July 2026 and GNSS repositioning put heavy tails on the errors: mean d²/3 rises while medians and coverage stay near nominal in LEO, so realism found on the selection window did not carry over. Operator covariance enters as supplied, labeled with its source.

7Dynamics and verification

HPOP's full force model, as the catalog and the conjunction screen run it¹⁰, beside the SP options a Vector Covariance Message (VCM) names³⁹:

HPOP's Orekit 13.1 suite⁴⁴ holds 72 cases on five orbits (400 km, 700 km sun-synchronous, GPS, geostationary, Molniya), each 24 hours, compared hourly on identical states, constants, daily Earth-orientation rows and space weather¹⁰. HPOP 1.3.0 (module SHA-256 9c24bf0e) integrates with RK78 at a relative tolerance of 1e-13 (point mass at 1e-15) and the steps named below; Orekit with Dormand–Prince 8(5,3) at 1e-14 and steps of at most 10 s:

At steps of up to 300 s, HPOP's own integration error is most of the difference: 1.8 cm over a day at 400 km (2.6 cm with JB2008 drag) and 1.6 cm at 700 km, against 0.03 mm for GPS satellites. With steps of 30 s the rows no longer depend on the step (a tolerance of 1e-15 with steps of 10 s moves them by under 0.2 mm), and the largest difference is in Molniya, 9.9 mm; 400 km and 700 km agree to 4.2 mm with drag and 1.7 mm without, and GPS and geostationary orbits to 0.2 mm. The rest is Earth orientation: Orekit applies the IERS Conventions' tidal and libration corrections to polar motion and UT1¹¹, and HPOP interpolates the daily rows. Against Orekit without those corrections the differences at 30 s are 0.6 mm for point mass, 1.1 mm without drag and 3.9 mm with it, and 0.6 mm in Molniya.

State-transition matrices agree within 2e-5 and parameter sensitivities within 1.5e-4 (relative), at steps of up to 300 s. Integrating Jacchia's diffusion equations numerically reproduces the closed forms of Jacchia-Roberts⁴⁵ to 1.6e-4.

Experiment V1 starts the propagator from ILRS orbits of four geodetic spheres (LAGEOS-1/2 and ETALON-1/2; 16 seeds) and IGS orbits of 32 GPS satellites (96 seeds), adds forces one set at a time, and compares each 72-hour run with the same product V1. GPS radiation pressure is a deliberately crude cannonball. Median (largest) 3D error:

The GPS maxima beyond a day are one satellite, NORAD 35752, in every force set. Of four pre-registered checks, two passed and two failed:

1. Passed: the two-body return, 0.8 mm.
2. Passed: the E-d bound at 24 hours, 246 m against 500 m.
3. Failed: an added force did not reduce every seed's error (14 violations, all without tesseral harmonics).
4. Failed: a 20×20 field without the Sun and Moon beat zonals alone for only 53 of 96 GPS seeds.

HPOP's resident path, which holds the catalog in memory, reproduces its execution path to 0.052 mm over four days, at 0.645 s per object-day on one thread¹⁰.

Association asks whether records describe one object; selection picks a solution for an epoch, interval and use; estimation derives a new one. Candidates come from provider crosswalks, such as Vimpel's datefirst file of Vimpel and NORAD numbers, international designators and native-identifier histories; names and bare numbers are not join keys. Compatibility is tested on normalized ephemerides over shared intervals. Each candidate link is compatible, rejected, ambiguous or insufficient, and accepted links stay reversible. Selection takes, per regime and horizon, the source with the lowest median error on a training window of at least 30 samples E3.

The VCM carries an SP state, its force settings and an equinoctial covariance³⁹. SDN's adapter reads a VCM into an HPOP request, transforming the covariance from equinoctial to Cartesian with an exact Jacobian computed by forward-mode dual numbers⁴⁷. The format states no covariance units, and no public definition was found. Four messages settle them:

1. The survey's ISS sample
2. An SP message for a geostationary orbit
3. An SP message for a GPS orbit
4. An SP message for an eccentric (e = 0.59) orbit

A VCM naming JBH09 runs as JB2008 on SET's indices, which the caller supplies.

Median 3D position error against precise orbits, by object class and age of the product:

The HAC's position errors are not published². The public figures: element sets in the HAC's own LEO conjunction regime (perigee above 500 km) err by 0.6–3 km from epoch to 72 hours⁴⁹; one ASW covariance shown as an illustration has σ of 8.3 m radial, 332 m in-track and 2.1 m cross-track at epoch³⁷; HASDM's density spread is 0.078 against JB2008's 0.148 (section 5.4).

Conjunction screening⁵⁰ takes from one catalog snapshot, per object:

An OMM supplies no covariance, so the catalog attaches one by the rule of section 2.2: built from the source's element-set errors against independent orbits and calibrated by regime and age, with its calibration label. Every event also carries the covariance-free maximum probability, which needs no covariance.

Appendix ATerms

Data credits

• IGS products, courtesy of the International GNSS Service and its analysis and data centres (Johnston, Riddell and Hausler 2017, doi:10.1007/978-3-319-42928-1). © Navigation Support Office at ESA/ESOC 2026.
• GFZ rapid MGEX orbits of the IGS Multi-GNSS Experiment (Montenbruck et al. 2017, doi:10.1016/j.asr.2017.01.011), obtained from NASA CDDIS (Noll 2010, doi:10.1016/j.asr.2010.01.018).
• ILRS data and products (Pearlman et al. 2019, doi:10.1007/s00190-019-01241-1), from the EUROLAS Data Center, DGFI-TUM (Noll et al. 2019, doi:10.1007/s00190-018-1207-2). NERC Space Geodesy Facility orbits; contains British Geological Survey materials © UKRI 2026, Open Government Licence v3.0.
• Contains modified Copernicus Sentinel data 2026.
• © ESA 2026; data provided by the European Space Agency: SW_SP3xCOM_2_ (doi:10.57780/esa-8579355), SW_DNSxPOD_2_ (doi:10.57780/esa-ef59315), GF_DNSxACC_2_ (doi:10.57780/esa-2559fd1).
• Licata, Mehta, Tobiska, Bowman and Pilinski (2021), CHAMP and GRACE-A density estimates with associated HASDM and JB2008 predictions, Zenodo, doi:10.5281/zenodo.4602380, CC BY 4.0.
• Source: USSPACECOM / 18th Space Defense Squadron, via Space-Track.org.
• SatNOGS Network observations (Libre Space Foundation; the station and observer named in each record), https://network.satnogs.org/, CC BY-SA 4.0.
• SpaceX Starlink public ephemerides, https://api.starlink.com/public-files/ephemerides/ (SpaceX). Planet Labs PBC orbital ephemerides, https://ephemerides.planet-labs.com/, © Planet Labs PBC, CC BY-NC 4.0. ISS trajectory: NASA JSC Flight Operations Directorate (U.S. Government work). China Manned Space Engineering Office, https://www.cmse.gov.cn/. Intelsat (SES) public ephemerides, https://my.intelsat.com/ephemeris/public. EUMETSAT.
• JSC Vimpel, http://spacedata.vimpel.ru/. SpaceMapper, https://spacemapper.cn/. CelesTrak, https://celestrak.org (T. S. Kelso). Data from J. McDowell, planet4589.org.
• The JB2008 solar and geomagnetic indices are provided for scientific use courtesy of Space Environment Technologies (https://spacewx.com/jb2008/). Kp, ap, Ap: GFZ Helmholtz Centre for Geosciences, CC BY 4.0 (Matzka et al. 2021, doi:10.5880/Kp.0001). Sunspot number: WDC-SILSO, Royal Observatory of Belgium, Brussels, CC BY-NC 4.0. F10.7: Dominion Radio Astrophysical Observatory and Natural Resources Canada. NOAA Space Weather Prediction Center (U.S. Government material).
• IERS EOP 20 C04 (IERS Earth Orientation Centre, Observatoire de Paris); finals2000A (IERS Rapid Service/Prediction Centre, U.S. Naval Observatory). JPL planetary ephemeris DE440 (Park et al. 2021, doi:10.3847/1538-3881/abd414), via NASA/JPL NAIF. EGM2008: NGA (Pavlis et al. 2012, doi:10.1029/2011JB008916). EGM96: NASA GSFC and NIMA (Lemoine et al. 1998). FES2004 (Lyard et al. 2006) as distributed with the IERS Conventions (2010).

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