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

This article introduces a gridless and fast 2-D 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 2-D 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. In addition, we use the Levinson–Durbin method for Toeplitz matrix inversion to reduce the computational load of the algorithm. This approach achieves a low computational complexity of O(N^2) 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.