The fundamental problem of line spectral estimation (LSE) using the expectation propagation (EP) method is studied. Previous approaches estimate the model order sequentially, limiting their practical utility in scenarios with large dimensions of measurements and signals. To overcome this limitation, a bilinear generalized LSE (BiG-LSE) method that concurrently estimates the model order is developed. The key concept involves iteratively approximating the original nonlinear model as a bilinear model through Taylor series expansion, with EP employed for inference. To mitigate computational complexity, the posterior log-pdfs are approximated to reduce the number of messages. BiG-LSE automatically determines the model order, noise variance, provides uncertainty levels for the estimates, and adeptly handles nonlinear measurements. Based on the BiG-LSE, a variant employing the von Mises distribution for the frequency is developed, which is suitable for sequential estimation. Numerical experiments and real data are used to demonstrate that BiG-LSE achieves estimation accuracy comparable to current methods.

翻译：本文研究了利用期望传播（EP）方法进行线谱估计（LSE）的基本问题。现有方法通常顺序估计模型阶数，这限制了其在测量和信号维度较大场景中的实际应用。为克服这一局限，本文提出了一种能同时估计模型阶数的双线性广义线谱估计（BiG-LSE）方法。其核心思想是通过泰勒级数展开，将原始非线性模型迭代近似为双线性模型，并采用EP进行推理。为降低计算复杂度，通过对后验对数概率密度函数进行近似以减少消息传递的数量。BiG-LSE能够自动确定模型阶数与噪声方差，为估计结果提供不确定性度量，并能有效处理非线性测量。基于BiG-LSE，本文进一步提出了一种采用冯·米塞斯分布对频率进行建模的变体，该变体适用于序列估计。数值实验与真实数据验证表明，BiG-LSE能达到与现有方法相当的估计精度。