Oscar Rodriguez Fernandez, OKAPI:Orbits GmbH; Adrian Diez Martin, OKAPI:Orbits GmbH; Njord Eggen, OKAPI:Orbits GmbH; Christopher Kebschull, OKAPI:Orbits GmbH; Alex Bush, OKAPI:Orbits GmbH
Keywords: SSA, SST, KF, OD, Orbit Determination, Kalman Filter, Covariance realism,
Abstract:
The rapid increase in Low Earth Orbit (LEO) traffic demands orbit determination (OD) solutions that are agile, resilient, and capable of processing sensor data from varied sources. Currently, the peak of the solar cycle is intensifying the density and instability of the upper atmosphere. In addition, the trend towards smaller and lighter satellites operating in lower orbits—particularly those around 500 km of altitude—exposes them to increased atmospheric drag. These factors complicate OD efforts, challenging the attainment of optimal accuracy and realistic covariance estimates which are critical for conjunction risk assessment.
In this work, we present a novel implementation of an Unscented Smith-Kalman Filter (USKF) designed for robust OD that includes dynamic consider parameter uncertainty estimation. The algorithm has been validated by processing data from Global Navigation Satellite System (GNSS) and Space Surveillance and Tracking (SST) sensors for several LEO satellites. The entire algorithm is implemented in FORTRAN for fast performance and employs the open sourced NPI Ephemeris Propagation Tool with Uncertainty Extrapolation (NEPTUNE) for high fidelity orbit propagation.
The USKF offers a more precise approach to modeling the process noise of the system as it is linked to the source of the uncertainty, for example, errors in drag acceleration modeling. Our methodology further extends this concept by incorporating dynamic consider-parameter modeling that adapts to time-varying uncertainties and can better deal with anomalous situations, like those triggered by solar storms. These are not captured by conventional methods, like Kalman Filters (KF) and other typical OD approaches, which can lead to filter divergence and/or underestimated covariances.
By harnessing advanced adaptive noise compensation techniques, our implementation of the USKF improves the state estimation accuracy over other alternative approaches. One of our key techniques is covariance matching, which continuously refines the uncertainties associated with consider parameters by comparing the prior consistency between the estimation error and the predicted covariance. The use of the Unscented Transform (UT) provides a more robust approach for modelling the effect of the consider parameters uncertainty, especially in high uncertainty scenarios such as very low Earth orbits and high solar activity. This approach ensures that uncertainty propagation accurately reflects the underlying physical processes, thereby improving overall model reliability.
By incorporating advanced modeling of drag forces and their associated uncertainties, this implementation of the USKF can promptly detect atmospheric disturbances caused by events such as solar storms. Consequently, users receive immediate notifications, allowing for rapid implementation of orbit corrections when required. When applied to a substantial number of satellites, this capability enables the derivation of real-time adjustments to the atmospheric model, thereby significantly enhancing the accuracy of orbit predictions, especially for short-term propagations.
An additional approach to increase the covariance realism is to account for measurement cross-correlation. With the increase in the number and performance of tracking sensors, such as radars, telescopes, and GNSS sensors, the number of measurements available for a given object and time interval has substantially increased over the last decade. Standard OD methods will assume that each individual measurement is a unique sample of the noise distribution. They neglect the possibility that measurements taken within a short interval are affected by a common bias. Based on this assumption, conventional OD approaches such as Weighted Least Squares (WLS) will usually lead to very small covariances that will often be very optimistic. In the case of KF, these will frequently cause filter divergence. By accounting for the cross correlation between observations, the covariance shrinking can be contained, leading to better filter performance. This is especially relevant in situations where continuous, frequent measurements are available, such as GNSS data.
One advantage of the USKF is its ability to deliver frequent OD updates, which facilitates continuous orbital updates of LEO objects in dynamic environments. This enhances situational awareness and timely decision-making in response to rapidly evolving space traffic conditions. The implemented approach is capable of fusing data from diverse sensor types, making it ideal for the nowadays SST environment where the number of sources is growing continuously.
In summary, this paper gives an overview of the USKF implementation and its ability to process diverse sensor data even in challenging environments, delivering state estimates and realistic covariance propagation. These capabilities ensure accurate conjunction risk assessments, regardless of the environmental difficulties.
Date of Conference: September 16-19, 2025
Track: Astrodynamics