On the Stratonovich approach for a satellite dynamics

摘要

In contrast to a vector non-linear stochastic differential equation (SDE) describing the satellite dynamics under the ‘fluctuating aerodynamic torque’, this paper analyses a second-order fluctuation equation for the radial perturbation about the given orbit. The second-order fluctuation equation for the radial perturbation has found its application for the satellite orbital stability. After accomplishing a phase space formulation, we arrive at the two-dimensional SDE. Most notably, the inaccurate choice of stochastic integral describing the satellite stochastic dynamics will have influence on their estimation, stability and control. For this reason, we develop a noise equation of the satellite dynamics in the Stratonovich setting. The satellite dynamics in the Stratonovich sense can be expressed equivalently in the It? setting by accounting additional correction terms in the system non-linearity term of the SDE. This paper develops the estimation theory of satellite dynamics via the Stratonovich calculus. The analytic findings are useful to the trajectory estimation of the orbiting satellite under the influence of atmospheric dust perturbations, where the observations are not available.