Acquisition of Visible Satellites Based on Antenna Arrays via Joint $\ell _{1,1}$-Norms Minimization

Abstract

This work tackles the acquisition of visible satellites based on an antenna array in the presence of impulsive noise. First, the joint angle and number estimation of visible satellites is formulated as a joint <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1,1}$</tex-math></inline-formula> -norms minimization problem by exploiting the spatial sparsity of visible satellites. Then, in order to obtain a closed-form solution, a generalized conjugate function for complex-valued matrix variable is introduced and the joint <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1,1}$</tex-math></inline-formula> -norms minimization is transformed into a Lagrangian dual function maximization. Furthermore, the dual ascent framework and subgradient technique are employed to obtain a suitable iterative solution, where the convergence rate and steady-state value can be flexibly adjusted. Numerical results are presented to demonstrate the effectiveness of the proposed approach.