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.

中文翻译：

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具有传播参数不确定性的多源定位的参数稀疏贝叶斯字典学习

基于接收信号强度（RSS）的源定位方法因其简单和低成本而广受欢迎。然而，这种方法高度依赖于其参数在实践中难以捕获的传播模型。在本文中，我们从叠加的 RSS 观测中估计多个同信道源的位置，同时联合推断参数传播模型。具体来说，我们首先将多源定位 (MSL) 问题建模为由未知源位置和传播参数进行参数化，然后将其重新表述为联合参数字典学习 (PDL) 和稀疏信号恢复 (SSR) 问题，从而解决通过具有迭代参数字典近似的稀疏贝叶斯学习。而且，为所提出的方法开发了一种快速迭代更新策略，以将高维大规模问题的复杂性从 $\mathcal {O}(MN^2)$ 降低到 $\mathcal {O}(MN)$，并且推导出 Cramér-Rao 下界 (CRLB) 来分析理论估计误差界。最后，讨论了假设的 MSL 模型和所提出的算法的一些重要特性，以及未来的研究方向。与最先进的基于稀疏性的 MSL 算法以及 CRLB 相比，大量的模拟表明了所提出方法的有效性和优越性。讨论了假设的 MSL 模型和所提出的算法的一些重要特性，以及未来的研究方向。与最先进的基于稀疏性的 MSL 算法以及 CRLB 相比，大量的模拟表明了所提出方法的有效性和优越性。讨论了假设的 MSL 模型和所提出的算法的一些重要特性，以及未来的研究方向。与最先进的基于稀疏性的 MSL 算法以及 CRLB 相比，大量的模拟表明了所提出方法的有效性和优越性。