Problem
Research questions and friction points this paper is trying to address.
Estimates model order concurrently
Reduces computational complexity via approximations
Handles nonlinear measurements effectively
Expectation Propagation based Line Spectral Estimation
🤖 AI Summary
To address the sequential determination of model order and insufficient robustness in high-dimensional line spectral estimation (LSE), this paper proposes the Bilinear Generalized LSE (BiG-LSE) method. BiG-LSE iteratively approximates the nonlinear observation model via Taylor expansion into a bilinear form and employs Expectation Propagation (EP) for joint Bayesian inference of frequencies, model order, and noise variance. It is the first LSE framework enabling fully automatic order selection and rigorous uncertainty quantification. To enhance sequential estimation accuracy, it adopts the von Mises distribution to model frequency priors. Furthermore, low-rank compression of posterior log-density messages significantly reduces computational complexity. Simulation and real-world experiments demonstrate that BiG-LSE achieves estimation accuracy comparable to state-of-the-art methods while exhibiting superior robustness and practicality under high-dimensional nonlinear measurements.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
EP-based bilinear LSE model
Taylor series for nonlinear approximation
Von Mises for frequency estimation
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