Adaptive grid OMP technique for the detection of low reflectivity moving objects in the presence of Doppler ambiguities

This paper proposes an efficient method for locating multiple off grid targets, whose responses lies in a high-dimensional space, in the presence of Doppler ambiguities. The detection and localization method is based on Orthogonal Matching Pursuit (OMP), a sparse linear decomposition technique for solving Compressed Sensing (CS) problems, combined with a gradient algorithm that adapts the grid to arbitrary positions. OMP algorithm is designed to find an approximation of a sparse signal discretized through determined positions, whereas, in practice, targets can be located anywhere within a continuous domain. The proposed method allows to recover the correct positions and amplitudes of targets located at off grid positions. The application of the proposed algorithm to ambiguous multi-burst radar signal demonstrates its efficiency for solving ambiguities. Numerical simulations show that this method reaches performance close to Cramer Rao bound for a wide range of signal-to-noise ratios.