Parametric Sparse Bayesian Dictionary Learning for Multiple Sources Localization With Propagation Parameters Uncertainty
Received signal strength (RSS) based source localization method is popular for its simplicity and low cost. However, this method is highly dependent on the propagation model whose parameters are hard to be captured in practice. In this paper, we estimate the locations of multiple co-channel sources from the superimposed RSS observations, while jointly inferring the parametric propagation model. Specifically, we first model the multiple sources localization (MSL) problem as being parameterized by the unknown source locations and propagation parameters, and then reformulate it as a joint parametric dictionary learning (PDL) and sparse signal recovery (SSR) problem, which is solved by sparse Bayesian learning with iterative parametric dictionary approximation. Moreover, a fast iterative update strategy is developed for the proposed method to reduce the complexity from $\mathcal {O}(MN^2)$ to $\mathcal {O}(MN)$ for high-dimensional large-scale problems, and the Cramér-Rao lower bound (CRLB) is derived to analyze the theoretical estimation error bound. Finally, some important properties of the assumed MSL model and the proposed algorithms, as well as the future research directions are discussed. Comparing with the state-of-the-art sparsity-based MSL algorithms as well as CRLB, extensive simulations show the effectiveness and superiority of the proposed methods.