Transition methods for stochastic simulation of parametric uncertainty in inverse problems of orbital dynamics - Avdyushev, V. A. (Celestial mechanics and dynamical astronomy)
The paper proposes an original nonlinear technique for stochastic simulation of the uncertainty in orbital parameters that arises in inverse problems of dynamical astronomy (orbit determination from observations) due to random observation errors. The technique is based on a vector differential equation describing transition lines from the dynamic state, obtained from observations, to virtual dynamic states of the uncertainty cloud in the space of orbital parameters at a given (initial) epoch. Using some numerical method for solving the differential equation, stochastic simulation for each virtual state is implemented as a sequence of piecewise state transitions. The new technique is tested in strongly nonlinear inverse problems of asteroid dynamics on the examples of one lost and two recently discovered objects. The results by the transition methods are compared with those obtained by the method of disturbed (noisy) observations, also known as the observational Monte Carlo method. A comparative analysis reveals a good agreement of the results, while the amount of calculations by the proposed technique is at least twice less.