AI 中文总结
本文提出基于张量的子空间方法用于多谐波源基音与DOA联合估计，通过保留张量结构优化子空间估计，仿真显示其在多场景下优于矩阵及张量列基线。
AI 中文摘要
针对多个谐波源的基音与到达方向（DOA）联合估计问题，本文提出一种基于张量的子空间方法。与将时空数据展开为单一矩阵的传统基于矩阵的方法不同，所提方法保留了多维汉克尔张量结构，并利用真实信号子空间满足的克罗内克积约束。通过将基于矩阵的子空间估计值投影到从模式展开的张量子空间中经验估计的克罗内克结构化信号约束集上，实现对该估计值的优化。除估计器本身外，本文还提供了一种非渐近理论，用于解释该张量优化在何种情况下优于矩阵基线。研究表明，使用真实克罗内克投影器的先知优化不会降低性能，将整体张量增益分解为先知增益与经验损失，并推导了复高斯噪声下整体张量增益为正的确定性及高概率充分条件。分析揭示了最优区间特性：当矩阵估计既非近乎完美也非过于不准确时，可获得最大的已验证增益。针对紧密间隔、谐波相关及相干源场景的仿真显示，所提方法提升了子空间精度及下游基音/DOA估计性能，且优于代表性的基于矩阵及张量列（tensor-train）的基线方法。
英文摘要
We propose a tensor-based subspace method for the joint estimation of pitch and direction of arrival (DOA) of multiple harmonic sources. Unlike conventional matrix-based approaches that unfold the spatio-temporal data into a single matrix, the proposed method preserves the multidimensional Hankel tensor structure and exploits a Kronecker product constraint satisfied by the true signal subspace. The matrix-based subspace estimate is refined by projecting it onto an empirically estimated Kronecker-structured signal cage obtained from mode-unfolded tensor subspaces. Beyond the estimator itself, we provide a non-asymptotic theory explaining when this tensor refinement improves the matrix baseline. We show that the oracle refinement using the true Kronecker projector is non-worsening, decompose the overall tensor gain into oracle gain and empirical loss, and derive deterministic and high-probability sufficient conditions for positive overall tensor gain under complex Gaussian noise. The analysis reveals a sweet-spot behavior: the largest certified gain occurs when the matrix estimate is neither nearly perfect nor too inaccurate. Simulations over closely spaced, harmonically related, and coherent-source scenarios show that the proposed method improves subspace accuracy and downstream pitch/DOA estimation, and also outperforms representative matrix and tensor-train-based baselines.
