A space object’s state estimate uncertainty is a piece of information paramount to at least four Space Situational Awareness (SSA) mission areas: conjunction assessment, measurement to track association, sensor tasking and scheduling, and manoeuvre detection.

However, many space surveillance data sources — e.g., Two-Line Elements (TLEs), Special Perturbations (SP) high-accuracy ephemerides — provide state estimates without associated uncertainty.

While modelling uncertain states with Gaussian-distributed random variables has its limitations in the context of orbital dynamics, notably under long propagation times, it remains a potent representation for SSA applications due to its simplicity of use. This paper will thus focus on the construction of covariance matrices, which provide second-order information about the underlying Gaussian distributions of the object states.

This paper first reviews synthetic covariance generation methods. These methods can be split into three categories: pseudo-observation paradigm, Conjunction Data Messages (CDMs) statistics, and ephemeris-sequence statistics methods. Independent and reusable techniques are identified across these categories. While the first two categories provide complementary approaches to ephemeris-sequence statistics methods, the last category is better suited for widespread, ready-to-use, synthetic covariance generation in operational scenarios.

This research compares the aforementioned synthetic covariance techniques and combines them in a unique ephemeris-sequence statistics-based synthetic covariance generation method. To begin with, a naïve, most basic, ephemeris-difference growth regression method is used as a baseline for comparison. This baseline computes 6x6 covariance predictions for SP ephemerides, assuming all Local Orbital Frame (LOF) components are independent.

The baseline has multiple apparent drawbacks. Five focus areas are selected to improve this baseline. For each, a well-suited technique from the literature review is tested. These techniques include the error growth model family — e.g., polynomial, exponential — tailored to each covariance component, LOF difference curvature correction, weighted ephemeris difference, robust least-squares regressions, and argument-of-latitude-dependant error growth model. Finally, a method combining the most effective techniques is proposed, demonstrating superior covariance realism.

All synthetic covariance generation methods are tested across multiple orbital regimes: Low Earth Orbit (LEO), Medium Earth Orbit (MEO), Highly Eccentric Orbit (HEO), and Geosynchronous Earth Orbit (GEO). SP ephemerides are used as input data. For some objects — e.g. calibration spheres, Global Navigation Satellite System satellites — reference cm-accuracy ephemerides are retrieved. Covariance realism is assessed by comparing the squared Mahalanobis distribution to a chi-squared distribution, both for cases with and without reference orbits.