Analysis of adaptive Gaussian mixture unscented kalman filter using sparse optical observations for initial orbit determination

The increasing amount of space debris poses significant threats to space assets. In order to avoid collisions with space debris, the acquisition of highly accurate and reliable orbital information of these threatening objects is necessary. A main caveat of optical observations (i.e., angles and angular rates) for space tracking is that the distance between the space object and the ground station is unknown. This factor can result in significant errors in obtaining the full information of the orbital state. One possible approach to address this is to introduce physical constraints to reduce the space of possible orbits, which is referred to as the admissible region (AR) technique. Additionally, for many real space debris tracking campaigns, limited observation times and short visible arcs lead to sparse observational data for a specific space object, which present more challenges to the initial orbit determination (IOD) problem. If there are large gaps between any two consecutive tracking arcs, the imperfect orbital dynamics with uncertain orbital parameters (e.g., area to mass ratio for atmospheric drag and solar radiation pressure) degrades the prediction accuracy and contributes to filter divergence. This paper presents an adaptive Gaussian mixture unscented Kalman filter (AGMUKF) to tackle this IOD problem. The initial orbital state is represented by a constrained AR or a probabilistic AR based on optical observations and additional physical constraints, i.e., semi-major axis and eccentricity. Thus, an AGMUKF can be initialised thereafter with splitting, pruning and merging of Gaussian mixture components. Both simulated and real observations are used for demonstration and analysis. The real data were collected at Mount Stromlo for different orbit scenarios. Efficacy of AGMUKF has been validated by preliminary IOD solutions initialised by two AR approaches.