Cold-Start Satellite Signal Acquisition Aided by an Antenna Array in the Presence of Outliers

In the cold-start mode, this work addresses the issue of signal acquisition for a satellite navigation receiver aided by an antenna array in the presence of outliers. First, the satellite signals acquisition is formulated as a problem of sparse matrix recovery in terms of
$\ell _{2,1}$
-norms minimization which encourages row sparsity of signal matrix and effectively suppresses outliers simultaneously. Then, an iterative reweighted framework and the Lagrange multipliers method with complex-valued conjugate gradient descent are employed to find a suitable solution. After that, to accelerate the convergence rate of the mean square error (MSE), an improved
$\ell _{2,1}$
-norms cost function with composite regularizers is devised, where several conjugate gradients of
$\ell _{2,1}$
-norms are derived in detail and convex optimization theory is employed to find the global minimum. At last, actual satellite almanac is downloaded to provide the information of the visible satellites and then numerical results are presented to demonstrate the effectiveness of the proposed methods.