Efficient Gridless Range–Angle Estimation for Active Sonar Systems Based on 2-D Fast Interior-Point Method

This paper introduces a gridless and fast 2- dimensional fast interior-point method (2D-FIPM) for range-angle estimation in active sonar systems. Traditionally, range-angle estimation relies on discretizing the domain of interest, where the use of predefined grids inevitably leads to grid mismatch issues. To overcome this drawback, we treat the range-angle estimation problem as a 2D gridless compressed sensing problem, which is formulated as a decoupled atomic norm minimization (DANM) problem. The developed 2D-FIPM enables the fast implementation of DANM and overcomes the grid dependence. The 2D-FIPM introduces an efficient method for determining the feasible domain of dual variables and updates both primal and dual variables through augmented Karush-Kuhn-Tucker conditions, leading to fewer iterations. Additionally, we use the Levinson-Durbin method for Toeplitz matrix inversion to reduce the conputational load of the algorithm. This approach achieves a low computational complexity of O(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) floating-point operations per iteration for an N+M order semidefinite matrix in DANM. Extensive numerical simulations demonstrate the algorithm's computational superiority, delivering excellent resolution and accuracy.