A SIMULATION TOOL FOR SPACE SITUATIONAL AWARENESS: NEAR EARTH OBJECTS

摘要

A simulation tool for Near Earth Objects (NEO) orbit determination by means of optical measurements is presented. The peculiarity of the simulator is the use of high order.methods based on Differential Algebra (DA) techniques. State-of-the art tools are mostly based on either linear methods or nonlinear Monte Carlo simulations. The main advantage of linear methods stays in their problem simplification, but their accuracy drops off rapidly for large uncertainty sets. Classical Monte Carlo simulations provide true statistics, but are computationally intensive. DA techniques are used to overcome the above issues, supplying the tools to compute arbitrary order derivatives of functions within a computer environment with limited computational effort. The availability of the high order Taylor expansions is exploited to manage problem uncertainties. The tool includes a simulator of optical observations, DA-based algorithms for NEO preliminary and accurate orbit determination. Angular measurements simulation is based on the propagation in time of initial asteroid state through multi-body dynamics; aberration, precession and nutation effects may be taken into account by the simulator. Preliminary orbit determination (POD) is based on Lambert's and Kepler's problems and uses the real solutions of the classical Gauss method 8~(th) order polynomial as first guesses of an iterative procedure. A better convergence with respect to Gauss method is achieved. Observations uncertainties are analytically mapped to the phase space as high-order multivariate Taylor polynomials. When more than three observations are available, the tool applies a high order Extended Kalman filter, initialized by the POD solution. The uncertainties related to the POD are propagated forward in time by exploiting the high order expansion of the flow of the dynamics. Thus, the initial covariance is nonlinearly and analytically propagated up to the next measurement. The performance of the tool is analysed by running the algorithms on a list of real Near Earth Asteroids and simulated topocentric observations.