Title: Maximum a posteriori estimation through simulated annealing for binary asteroid orbit determination,
Abstract: This paper considers a new method for the binary asteroid orbit determination
problem. The method is based on the Bayesian approach with a global
optimisation algorithm. The orbital parameters to be determined are modelled
through an a posteriori distribution made of a priori and likelihood terms. The
first term constrains the parameters space and it allows the introduction of
available knowledge about the orbit. The second term is based on given
observations and it allows us to use and compare different observational error
models. Once the a posteriori model is built, the estimator of the orbital
parameters is computed using a global optimisation procedure: the simulated
annealing algorithm. The maximum a posteriori (MAP) techniques are verified
using simulated and real data. The obtained results validate the proposed
method. The new approach guarantees independence of the initial parameters
estimation and theoretical convergence towards the global optimisation
solution. It is particularly useful in these situations, whenever a good
initial orbit estimation is difficult to get, whenever observations are not
well-sampled, and whenever the statistical behaviour of the observational
errors cannot be stated Gaussian like.