• asteroid orbit determination
• asteroid 2008TC3
• collision probability
• MCMC ranging
• Monte Carlo ranging
• random-walk ranging

The determination of preliminary asteroid orbits and collision probabilities is a critical aspect of planetary defense and space situational awareness, particularly for near-Earth objects (NEOs) that pose potential threats to Earth. For poorly observed objects, orbital uncertainties are often significant, and conventional deterministic techniques—which produce a single orbital solution with a confidence region compatible with observations—frequently fail to capture the true extent of these uncertainties.
This thesis explores advanced statistical and computational methods for addressing the inverse problem of orbit determination with a focus on Bayesian frameworks and probabilistic techniques. Key contributions include the development and application of Monte Carlo (MC) ranging and Markov-Chain Monte Carlo (MCMC) ranging methods to overcome challenges posed by sparse or noisy observational data. By propagating sampled orbits into the future, these methodologies allow for robust evaluation of Earth collision risks over specified time intervals.
The Bayesian framework enables a detailed probabilistic characterization of orbital uncertainties by incorporating prior information and accounting for observational noise, assumed to follow a multivariate Gaussian distribution. However, computing arbitrary a posteriori probability density function (p.d.f.) of orbital elements can be challenging, even under the simplifying assumption of Gaussian noise statistics. To address this, the MC ranging method is introduced as a versatile tool for unbiased sampling of the orbital-element phase space. This method generates a large set of Monte Carlo orbits by sampling random values for the topocentric range within a defined domain centered on the maximum likelihood orbit. Depending on the availability of a preliminary orbit, either a restricted or unrestricted sampling approach is employed, treating the Bayesian a priori p.d.f. as constant or variable, respectively.
The thesis further presents the MCMC ranging method, which leverages Monte Carlo techniques combined with the Metropolis-Hastings algorithm to construct a Markov chain that converges to the target a posteriori distribution. Diagnostic tools, such as burn-in periods, acceptance probability checks, and convergence analyses, are employed to ensure proper convergence to the stationary distribution. Additionally, the random-walk ranging method is introduced as an alternative technique designed to enable uniform sampling of the phase space up to a limiting Δχ2-value, improving accuracy for multimodal distributions.
A case study on asteroid 2008TC3, the first asteroid observed before its impact with Earth, demonstrates the effectiveness of these methodologies. Using an automated MCMC ranging approach, the collision probability is reliably estimated despite the extremely limited observational arc. However, the study highlights a strong sensitivity of collision probability estimates to assumptions about astrometric noise, underscoring the importance of improved noise characterization.
The methods discussed in this work demonstrate the potential of probabilistic approaches for initial orbit determination and collision risk assessment of asteroids with short observational arcs or limited numbers of observations. By balancing accuracy and computational efficiency, these methodologies provide a foundation for more effective follow-up strategies and contribute to a deeper understanding of the dynamical behavior of NEOs. Nonetheless, challenges remain, such as optimizing convergence criteria and managing long Markov chains in complex scenarios, offering opportunities for future refinement.