We consider signal detection in subspace interference with partial prior knowledge of the subspace. The problem was recently considered by Li et al., where a subspace knowledge with learning (SKL) Bayesian model was proposed to leverage partial and uncertain knowledge of the subspace bases. The SKL, however, is based on the assumption that the subspace bases are a subset of a known overdetermined dictionary defined on a densely sampled frequency grid. Due to the so-called grid mismatch problem, i.e., the subspace bases may not be exactly on the frequency grid, there is a need to develop solutions that can exploit approximate prior knowledge, i.e., knowledge of frequency grid points close to the true frequencies but the latter themselves. In this paper, we extend the work by Li et al. and develop a modified SKL (mSKL) algorithm to exploit partial, approximate, and uncertain prior knowledge for subspace estimation and target detection. The mSKL is a Bayesian inference algorithm that can reject incorrect subspace bases, recover missing bases, and benefit approximately correct bases in the prior knowledge set. For computational efficiency, the recently introduced generalized approximate message passing (GAMP) is employed in the mSKL for efficient update of some posteriors. The resulting scheme, referred to as the mSKL-GAMP, is shown to offer competitive subspace recovery and target detection performance over a range of alternative methods in various scenarios with different grid mismatch levels.

中文翻译：

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具有不确定部分先验知识的自适应子空间信号检测：离网问题与高效实现

我们考虑子空间中的信号检测干扰与子空间的部分先验知识。Li 等人最近考虑了这个问题，其中提出了具有学习 (SKL) 贝叶斯模型的子空间知识，以利用子空间基的部分和不确定知识。然而，SKL 基于以下假设：子空间基是在密集采样频率网格上定义的已知超定字典的子集。由于所谓的网格失配问题，即子空间基可能不完全在频率网格上，需要开发可以利用近似先验知识的解决方案，即接近真实频率的频率网格点的知识但后者本身。在本文中，我们扩展了 Li 等人的工作。并开发一种改进的 SKL (mSKL) 算法来利用部分，用于子空间估计和目标检测的近似和不确定先验知识。mSKL 是一种贝叶斯推理算法，可以拒绝不正确的子空间基，恢复丢失的基，并使先验知识集中近似正确的基受益。为了计算效率，在 mSKL 中采用了最近引入的广义近似消息传递 (GAMP)，以有效更新一些后验。由此产生的方案，称为 mSKL-GAMP，显示出在具有不同网格失配水平的各种场景中，通过一系列替代方法提供具有竞争力的子空间恢复和目标检测性能。并受益于先验知识集中近似正确的基础。为了计算效率，在 mSKL 中采用了最近引入的广义近似消息传递 (GAMP)，以有效更新一些后验。由此产生的方案，称为 mSKL-GAMP，显示出在具有不同网格失配水平的各种场景中，通过一系列替代方法提供具有竞争力的子空间恢复和目标检测性能。并受益于先验知识集中近似正确的基础。为了计算效率，在 mSKL 中采用了最近引入的广义近似消息传递 (GAMP)，以有效更新一些后验。由此产生的方案，称为 mSKL-GAMP，显示出在具有不同网格失配水平的各种场景中，通过一系列替代方法提供具有竞争力的子空间恢复和目标检测性能。