Low Earth orbit (LEO) satellites are leveraged to support new position, navigation, and timing (PNT) service alternatives to GNSS. These alternatives require accurate propagation of satellite position and velocity with a realistic quantification of uncertainty. It is commonly assumed that the propagated uncertainty distribution is Gaussian; however, the validity of this assumption can be quickly compromised by the mismodeling of atmospheric drag. We develop a machine learning approach that corrects error growth in the argument of latitude for a diverse set of LEO satellites. The improved orbit propagation accuracy extends the applicability of the Gaussian assumption and modeling of the errors with a corrected mean and covariance. We compare the performance of a time-conditioned neural network and a Gaussian Process on datasets computed with an open source orbit propagator and publicly available Vector Covariance Message (VCM) ephemerides. The learned models predict the argument of latitude error as a Gaussian distribution given parameters from a single VCM epoch and reverse propagation errors. We show that this one-dimensional model captures the effect of mismodeled drag, which can be mapped to the Cartesian state space. The correction method only updates information along the dimensions of dominant error growth, while maintaining the physics-based propagation of VCM covariance in the remaining dimensions. We therefore extend the utility of VCM ephemerides to longer time horizons without modifying the functionality of the existing propagator.
Figures & tables
Fig. 1: Machine learning model predicts errors and variance in the argument of latitude to correct both the propagated orbit and covariance for a variety of LEO orbit and satellite types.
Fig. 2: Orbit propagation correction pipeline using VCMs, open source SP propagator, and machine learning model.
Parameter
Description
Epoch time (UTC)
Orbital estimate epoch time, expressed in Coordinated Universal Time.
J2K Pos/Vel X-Y-Z ( km , km/s )
The position and velocity vector components of the satellite expressed in Earth-Centered Inertial reference frame.
Ballistic Coef. ( m2/kg )
Estimated ballistic coefficient at epoch.
Solar Rad Press Coeff ( m2/kg )
Estimated solar radiation pressure coefficient at epoch.
Geo Pot
Degree and order of geopotential model used.
Drag
Atmospheric density model used.
TABLE I: Summary of VCM parameters used in modeling and dataset generation
Fig. 3: Accelerations due to individual force models in Orekit orbit propagator over various altitudes for an example satellite in an initially circular orbit with a ballistic coefficient of 0.13 m2/kg .
Perturbation Force Models
Solar Radiation Pressure
70 × 70 Gravity (EGM-96)
Solid Earth Tides
Sun Third Body
Moon Third Body
Atmospheric Drag (NRLMSISE-00)
TABLE II: Orekit Force Models
Fig. 4: Example of error growth for propagation of a single VCM (NORAD ID 47). True AOL error maps to predominantly along-track position and radial velocity dimensions. Errors in the remaining dimensions are caused by errors in other orbital elements and therefore are not captured by argument of latitude.
Fig. 5: Over 95% of the norm position error is captured by the argument of latitude after 5 day propagation (NORAD ID 47).
Fig. 6: AOL errors used to train the ML models consisting of 50 VCMs propagated 7 days for 800 satellites.
σRr km
σRs km
σRw km
σVr m/s
σVs m/s
σvw m/s
0.23
12
0.013
13
0.043
0.017
TABLE III: Validation dataset standard deviations in RSW frame after seven days of propagation
Fig. 7: TCNN - Corrected and Uncorrected Error Distributions Over Time.
Fig. 8: TCNN - Error reduction in all dimensions of ECI Cartesian frame after AOL correction.
Dataset
σRs km
σVr m/s
σ∥R∥ km
σ∥V∥ m/s
% DMu,C
% DM[R,V],C
Uncorrected
12
13
11
12
-
7.7
TCNN
6.2
6.8
5.5
6.1
95
81
HGP
6.8
7.5
6.1
6.7
97
81
TABLE IV: Correction performance for HGP and TCNN for 7 day propagation
Fig. 9: Covariance realism improvement after AOL correction in ECI Cartesian frame.
Dataset
σRs km
σVr m/s
σ∥R∥ km
σ∥V∥ m/s
% DMu,C
Uncorrected
12
13
11
12
-
TCNN
11
12
11
12
64
HGP
9.9
11
9.3
10
96
TABLE V: Correction performance for HGP and TCNN for 7 day propagation with time generalization
Uncertainty propagation studies how measurement, model, and data uncertainty flows through computations and affects downstream predictions and decisions.
Reliable localization in GNSS-denied environments remains a fundamental challenge for intelligent vehicles, as inertial navigation systems accumulate unbounded drift without external correction. Existing approaches provide drift correction through dedicated infrastructure, expensive external sensors, or complex multi-sensor fusion, each introducing practical deployment barriers. We propose Evidential Velocity Correction using Mamba (EVC-Mamba), a learning-based architecture that transforms onboard vehicle sensor data into a virtual velocity sensor for IMU drift correction without additional hardware. A Mamba-based selective state space model captures the temporal dynamics of vehicle motion, while evidential deep learning with a Normal-Inverse-Gamma distribution provides principled uncertainty quantification. The resulting uncertainty-aware velocity estimate is incorporated as a virtual correction measurement into an Error-State Extended Kalman Filter to reduce position drift. Evaluation on real-world vehicle data demonstrates that inertial navigation using the proposed velocity correction achieves localization accuracy within 10% of a dedicated external velocity sensor across different outage durations. The proposed architecture supports real-time onboard deployment at 40 Hz on edge hardware, enabling reliable localization during prolonged GNSS outages.
Abinav Kalyanasundaram, Karthikeyan Chandra Sekaran, Wolfgang Utschick +1
AImotion Bavaria, Technische Hochschule Ingolstadt, Germany · Technische Universität München, Germany
Low Earth Orbit (LEO) satellite Doppler measurements offer an alternative source of positioning information for Internet of Things devices when Global Navigation Satellite System signals are unavailable. Conventional local optimisation methods depend on an accurate initial position and can fail during a complete cold start. We propose an initialization-free LEO Doppler positioning framework based on semidefinite relaxation. The method reformulates the nonlinear positioning problem into a semidefinite programme to obtain a receiver position estimate without prior location knowledge. We analyse relaxation tightness under noiseless conditions and derive sufficient noise bounds under parameter disturbances. Simulations and field experiments using opportunistic Iridium-NEXT signals evaluate initialization sensitivity, positioning accuracy and computational cost. In the field experiment, the proposed method achieves a three-dimensional positioning error of 140 m without an initial position, whereas local solvers converge to poor solutions under large initial offsets. Using the semidefinite estimate to initialise Gauss-Newton or Dog-Leg reduces the positioning error to 130 m. The framework provides a cold-start initialization stage for subsequent local refinement in opportunistic LEO positioning. The implementation and datasets are publicly available to support reproducibility and further research.
Baoshan Song, Weisong Wen, Qi Zhang +4
The Hong Kong Polytechnic University, Hong Kong SAR, China
Neural residuals can improve satellite evapotranspiration (ET) estimates, but selectors must predict when a correction helps and reject unsupported inputs. We evaluate ten-member models on 16,366 flux-tower observations from 151 stations paired with OpenET, across nine rolling years and five spatial folds. At one held-out station, Gain accepted corrections on all 32 physically invalid records: it predicted a mean benefit of 0.83 mm/day, but the corrections increased mean absolute error by 21.6 mm/day versus OpenET. On spatially held-out unit errors, SupportGain reduced station-macro MAE versus Gain by 0.148 mm/day under wind x3.6 (simultaneous 95% interval, 0.070 to 0.226), with 9.3% acceptance versus Gain's 51.8%; on clean inputs, its 0.006 mm/day advantage had an interval that includes zero. These fault analyses are exploratory; none of 40 preplanned temporal comparisons passed Holm correction, while a separate predeclared cropland contrast found 0.041 mm/day lower station-macro MAE with crop-only training (95% interval, 0.009 to 0.079).