Stratonovich framework into Markovian satellite dynamics of Carleman-based filtering using energy function observables approach

Abstract

In this paper the satellite system in which fluctuating aerodynamic torque and the radial perturbation about the pitch motion of orbit is analyzed. The objectives of the paper are three-fold. The first objective is the ‘Carleman linearization representation into the nonlinear stochastic evolution of the Markov process’. The second is to filter process and measurement noises in the satellite dynamics parameters in the Carleman setting. The third is to find the stability and convergence condition of satellite dynamics. The first is achieved by unifying the generating function, Carleman embedding, Itô stochastic differential rules and the finite closure with Kronecker algebra. Concerning the second objective, we recast the finite-dimensional Stochastic Differential Equations (SDE) of the satellite dynamics into a finite system of bilinear SDE via the Carleman embedding. The third objective is to achieve the Lyapunov function and asymptotic stability condition for the satellite stochastic dynamics involving the ‘Stratonovich differential’. In this paper, we demonstrate the utility of the satellite dynamics filtering in the Carleman-based filtering via ‘its convergence analysis as well as its superiority with available methods’, i.e., the benchmark extended Kalman filter, Gaussian second-order filter and Kushner–Stratonovich higher-order filter. From simulation performed it can be said that the Carleman-based filtering is superior than other benchmark filters in terms of their Absolute Filtering Error (AFE) of conditional means and conditional variances of the satellite dynamics states.