Localization and bearing estimation via structured sparsity models

Recent work has leveraged sparse signal models for parameter estimation purposes in applications including localization and bearing estimation. A dictionary whose elements correspond to observations for a sampling of the parameter space is used for sparse approximation of the received signals; the resulting sparse coefficient vector's support identifies the parameter estimates. While increasing the parameter space sampling resolution provides better sparse approximations for arbitrary observations, the resulting high dictionary coherence hampers the performance of standard sparse approximation, preventing accurate parameter estimation. To alleviate this shortcoming, this paper proposes the use of structured sparse approximation that rules out the presence of pairs of coherent dictionary elements in the sparse approximation of the observed data. We show through simulations that our proposed algorithms offer significantly improved performance when compared with their standard sparsity-based counterparts. We also verify their robustness to noise and applicability to both full-rate and compressive sensing data acquisition.