This paper presents a novel efficient method for gridless line spectrum estimation problem with single snapshot and sparse signals, namely the gradient descent least squares (GDLS) method. Conventional single snapshot (a.k.a. single measure vector or SMV) line spectrum estimation methods either rely on smoothing techniques that sacrificing the range and/or azimuth resolution, or adopt the sparsity constraint and utilize compressed sensing (CS) method by defining prior grids and resulting in the off-grid problem. Recently emerged atomic norm minimization (ANM) methods achieved gridless SMV line spectrum estimation, but its computational complexity is extremely high; thus it is practically infeasible in real applications with large problem scales. Our proposed GDLS method reformulates the line spectrum estimations problem into a least squares (LS) estimation problem and solves the corresponding objective function via gradient descent algorithm in an iterative fashion with efficiency. The convergence guarantee, computational complexity, as well as performance analysis for evenly distributed antenna array case are discussed in this paper. Numerical simulations show that the proposed GDLS algorithm outperforms the state-of-the-art methods e.g., CS and ANM, in terms of estimation performances. It can completely avoid the off-grid problem, and its computational complexity is significantly lower than ANM. Our method has been tested in tomographic SAR (TomoSAR) imaging applications via simulated and real experiment data. Results show great potential of the proposed method in terms of better cloud point performance and eliminating the gridding effect.

Due to its miniature size and single-pass nature, Unmanned Aerial Vehicle (UAV)-borne array Synthetic Aperture Radar (SAR) is capable of obtaining three-dimensional (3D) electromagnetic scattering information with low cost and high efficiency, making it widely applicable in various fields. However, the limited payload capacity of the UAV platform results in a limited number of array antennas and affects the 3D resolution. This paper proposed a 3D imaging method for UAV-borne SAR based on nested difference co-array and azimuth multi snapshot. We first designed an antenna arrangement based on nested arrays, generating a virtual antenna twice as long as the original one. Then we used difference co-array method for 3D imaging. The required multi-snapshot data is obtained through azimuth down-sampling, rather than the traditional spatial averaging methods. Due to the slow flight of the UAV, this method can generate multiple SAR images without affecting the two-dimensional resolution. Based on simulation and real data verification, the proposed algorithm overcomes the problem of two-dimensional resolution decline caused by traditional spatial averaging methods and improves the third dimension resolution ability, achieving half of the Rayleigh resolution theoretically.

Due to its miniature size and single-pass nature, Unmanned Aerial Vehicle (UAV)-borne array synthetic aperture radar (SAR) is capable of obtaining three-dimensional (3D) electromagnetic scattering information with a low cost and high efficiency, making it widely applicable in various fields. However, the limited payload capacity of the UAV platform results in a limited number of array antennas and affects 3D resolution. This paper proposes a 3D imaging method for UAV-borne SAR based on nested difference co-arrays and azimuth multi-snapshots. We first designed an antenna arrangement based on nested arrays, generating a virtual antenna twice as long as the original one. Then, we used a difference co-array method for 3D imaging. The required multi-snapshot data were obtained through azimuth down-sampling, rather than traditional spatial averaging methods. Due to the slow flight of the UAV, this method could generate multiple SAR images without affecting the two-dimensional resolution. Based on simulations and real data verification, the proposed algorithm overcomes the problem of two-dimensional resolution decline caused by traditional spatial averaging methods and improves three-dimensional resolution ability, theoretically achieving half the Rayleigh resolution.