Improved orbit predictions using two-line elements

1 Introduction

• Collision avoidance needs sufficiently precise predictions to avoid an unwieldy number of maneuvers, and avoiding collisions only for maneuverable spacecraft does not suffice to curb debris growth.The introduction identifies debris removal and collision avoidance as alternatives to debris mitigation.Source: §1 · p. 2
• TLE/SGP4 predictions produce many low-probability potential collisions, while debris-debris conjunctions compound the imprecision because both objects are uncertain.The paper argues that this makes maneuvering to avoid potential collisions impractical.Source: §1 · p. 2
• The research target is to improve predictions for non-maneuvering objects using only historical TLEs, toward operational conjunction assessment for collision avoidance.The paper frames this as a response to the TLE/SGP4 accuracy problem.Source: §1 · p. 2
• The paper previews an approach and accuracy assessment, requirements for extending it to the full space-object catalog, and a proposed debris-debris avoidance method.It also notes that collisions threaten spacecraft, astronauts, and near-Earth space, with cumulative collisions consistent with predictions of a runaway chain reaction.Source: §1 · p. 2

2 Method: TLE orbit fitting and propagation

• The approach adapts prior TLE-error work by fitting predicted positions from historical TLEs rather than quantifying SGP4 propagation errors.The fitted orbit is compared with precision orbital ephemeris data from the International Laser Ranging Service.Source: §2 · p. 3
• A high-precision propagator and batch least-squares differential correction fit an orbit to TLE-derived pseudo-observations, which is then propagated forward.The method's prediction accuracy is assessed against precision orbital ephemeris data.Source: §2 · p. 3
• The initial fitting window is 10 days and the subsequent prediction period is 30 days; TLEs from the prediction period are reserved for validation and testing.Only TLEs within the fitting period enter the fitting process.Source: §2 · p. 3
• About 100 equally spaced state vectors are generated from fitting-period TLEs, and correction minimizes radial, in-track, and cross-track relative-position RMS error.The force model includes 60 × 60 EGM2008 gravity, solar and lunar point masses, atmospheric drag, and solar radiation pressure; solar F10.7 and Ap are fixed at fitting-period averages.Source: §2 · pp. 3–4

• The four non-manoeuvring test spacecraft were selected partly to span orbital altitudes; 50 randomized-start runs were summarized for 2004 and 1994.Figure 3 limits the SGP4 comparison to 10 days, or 5 days for rapidly diverging Starlette.Source: §3 · p. 4, Table 1 · p. 4, Figure 2 · p. 6
• For Stella and Etalon-2, SGP4 predictions departed rapidly from truth, while the fitted and propagated orbits maintained higher accuracy, particularly long term.Source: §3 · p. 4, Figure 1 · p. 5
• Truth data were not used for fitting or hyperparameter tuning, and errors under one day were dominated by TLE bias that the method could not remove.Source: §3 · pp. 4, 6, 7
• Median error growth stayed below 150 m/day for Stella and 30 m/day for Etalon-2; 30-day median-error ratios averaged 15, ranging from 3 to 50.Source: §3 · p. 5
• 3 km at 30 days out (~100 m/day) was typical for our method, versus typical growth of 1,500 m/day for TLEs propagated with SGP4.Source: §3 · pp. 4–5, Figure 2 · p. 6
• The method improved prediction accuracy by about one order of magnitude in all three RIC directions, likely reducing false-positive conjunctions by 2 to 3 orders of magnitude.Source: §3 · pp. 5–6

4 Fitting Debris objects

• Future TLEs beyond the fitting period can proxy for truth when debris-only fitting and validation lack precision ephemeris data.The paper notes no publicly available high-accuracy debris trajectory and proposes refining debris predictions from TLEs alone.Source: §4 · p. 8
• Manual experiments suggested that optimal fitting periods differ by orbit category, prompting per-object cross-validation to select the interval.The cross-validation investigation uses TLEs for both fitting and validation.Source: §4 · pp. 8–9
• A 10-day fitting period was optimal for Ajisai against both future-TLE proxy and POE truth, for predictions 5, 10, and 30 days ahead.Figure 4 compares prediction error against fitting period; each box-and-whisker plot summarizes 50 runs from random 1994 starting dates.Source: §4 · p. 9, Figure 4 · p. 9
• Debris application also requires solving for area-to-mass ratio and validating it using future TLEs; those experiments were still underway.Source: §4 · p. 9

5.1 Methodological Improvements

• Further accuracy work could optimize fitting-point number and weighting, filter outliers, and refine TLE corrections by orbital regime.The paper also notes that global TLE transformations may improve TLE/SGP4 accuracy.Source: §5.1 · p. 10
• Testing on actual known conjunctions was proposed to assess the scheme’s efficiency for conjunction assessment.The authors assign this test to future work.Source: §5.1 · p. 10

5.2 Computational Scaling

• About 1 minute on approximately 200 CPU cores sufficed for 7-day all-on-all checks; a simulated 2.5-million-object catalog took about 40 minutes.The simulated S-band fence catalog contained pseudo-TLEs for objects of size ≥2 cm.Source: §5.2 · p. 10

5.3 A New Scheme for Debris-Debris collision avoidance

• An along-track ΔV of 1 cm/s gives about 1 km/day displacement; two suitably oriented radiation-pressure events produced the proposed scale of debris displacement.The modeled irradiation was 10 times solar radiation for 10 minutes and yielded more than 0.1 km/day along track for a typical debris object.Source: §5.3 · p. 11
• A ground-based 10 kW-class laser could conceivably provide the radiation pressure, but beam divergence and tracking require engineering analysis.The example considers an object with area below 1 m² in SSO.Source: §5.3 · p. 11
• The cited results imply that debris-debris avoidance for five additional carefully selected objects per year could curb debris-field growth.The paper says further avoidance could eventually reduce net debris density below a critical level as atmospheric drag continues to remove objects.Source: §5.3 · p. 11

6 Conclusions

• TLE-only fitting and propagation could potentially make initial conjunction analysis accurate enough for an operationally viable collision-avoidance system.The conclusion says operational use would require additional data, including the uncorrelated objects that account for approximately 30% of potential LEO conjunctions.Source: §6 · p. 11
• All-on-all conjunction assessment was demonstrated as possible with moderate computing infrastructure, including for an expected larger tracked-object catalog.Source: §6 · p. 12
• Debris-debris collision avoidance using externally induced small radiation-pressure maneuvers may be possible and could negate the need for large-scale debris removal.The proposed approach uses ground-based lasers in the 10 kW class.Source: §6 · p. 12