Expectation Propagation based Line Spectral Estimation

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.