Basis pursuit over continuum applied to range-Doppler estimation problem

Sparse estimation and compressive sensing techniques have been recently considered for radar estimation problems. It is frequently observed that these methods are robust to model uncertainties and substantially improve performance in scenarios with a low signal-to-noise. However, since current sparsity-based techniques are computationally costly and require a suitable discretization (grid), which strongly restricts resolution, they practically receive less attention. In this work, we present an application of a new sparsity-based technique to the specific problem of range-Doppler estimation. The method, generalizing basis pursuit, is less computationally complex and its performance is independent of the grid selection. We demonstrate that the proposed technique can improve estimation performance in difficult cases, as compared to the SAGE technique.