Sparse signal processing techniques, such as compressed sensing, are commonly employed in tomographic synthetic aperture radar (TomoSAR) imaging due to the sparsity present in the elevation direction. However, classical compressed sensing methods, such as ℓ ₁ norm regularization and orthogonal matching pursuit (OMP), suffer from the off-grid effect. Specifically, they discretize the elevation axis into multiple grids and assume that scatterers are located precisely on the grids, leading to reconstruction results that deviate from the true heights of the scatterers. Although gridless compressed sensing methods, such as atomic norm minimization (ANM), have achieved gridless reconstruction in specific scenarios, they face challenges such as the requirement of uniformly distributed baselines and large computational cost. In this paper, we propose a gridless compressed sensing method based on the alternate descent conditional gradient (ADCG) kernel for TomoSAR inversion, and compare it with ANM, iterative soft thresholding (IST), and OMP. We show through numerical simulations and experimental results that our proposed method is applicable not only to scenarios with uniformly distributed baselines, but also to scenarios with non-uniformly distributed baselines, and resolves the off-grid effect in both cases. Finally, we demonstrate the effectiveness of our proposed method by implementing gridless reconstruction using an actual dataset of urban buildings in Yuncheng.

In automotive millimeter-wave (MMW) radar systems, achieving high-precision direction of arrival (DOA) estimation with a limited number of array elements is a crucial research focus. Compressive sensing (CS) techniques have been demonstrated to offer superior performance in DOA estimation compared to spectral estimation methods. However, traditional CS methods suffer from an off-grid effect, which causes their reconstruction results to deviate from the actual positions of the signal sources, thereby reducing the accuracy. Currently, as a gridless method, atomic norm minimization (ANM) has shown effectiveness in DOA estimation for uniform linear arrays (ULAs). However, the performance of ANM is suboptimal in non-uniform linear arrays (NULAs), and their computational efficiency is not satisfactory. In this paper, we propose a novel algorithm for DOA estimation in NULA, drawing inspiration from the alternating descent conditional gradient algorithm framework. First, we construct an atomic set based on the observation scene and select the atoms with the highest correlation to the residuals as potential signal sources for global estimation. Then, we construct a mapping function for the signal sources in the continuous domain and perform conditional gradient descent in the neighborhood of each signal source, addressing the bias introduced by the off-grid effect. We compared the proposed algorithm with ANM, Iterative Shrinkage Thresholding (IST), and Multiple Signal Classification (MUSIC) algorithms. Simulation experiments validate that the proposed algorithm effectively addresses the off-grid effect and is applicable to DOA estimation in coprime and random arrays. Furthermore, real data experiments confirm the effectiveness of the proposed algorithm.