Low Signal to Noise State Space Modelling Using Simulation Based Inference

The challenges of detecting and characterizing very small objects in Medium Earth Orbit (MEO), Geostationary Orbit (GEO), or beyond GEO (xGEO) regimes are significant and have been recognized as an area of strategic importance. Developing high-precision Space Situational Awareness (SSA) solutions is critical in addressing these challenges, especially as current methodologies often fall short in certain key aspects. Optical systems, while adaptable to distant orbit regimes, face limitations due to low signal-to-noise ratios. Not enough light reflected off the Resident Space Object (RSO) reaches the telescope to be detectable in an exposure or frame. Various track-before-detect (TBD) approaches have been proposed in the literature, largely based on variations of hidden Markov models. Approaches such as Kalman filters and multi-Bernoulli filters, as well as variations thereof, provide excellent solutions for point estimation of the maximum a posteriori solutions of the underlying state space model. Another approach to state space modeling is through posterior sampling methods such as Markov Chain Monte Carlo (MCMC). While significantly more burdensome computationally, sampling techniques provide a richer understanding of the state space model's posterior distribution. This can be particularly useful in the presence of non-Gaussian noise and non-linear state space models. This paper focuses on a recent development in sampling theory, simulation-based inference (SBI). We show that SBI techniques, in particular neural posterior estimation, can not only accurately constrain the underlying orbital state space model in very low signal-to-noise conditions but can also be shown to be computationally less intensive than classic MCMC approaches. This allows for a full recovery of the state space's posterior distribution while making the approach sufficiently computationally efficient to be used for regular post-processing of state space models.