Adaptive nonlinear group delay mode estimation

Abstract

The decomposition of non-stationary signals remains a challenge in a wide variety of fields. Especially, the impulse or cross-mode signals are difficult to be reconstructed by recent methods due to their transient characteristic. Moreover, most methods rely heavily on the user-defined settings of the regularized parameter for the convex optimization algorithm. In this work, an adaptive nonlinear group delay mode estimation (ANGDME) algorithm is proposed by exploiting the sparsity of signals formulated as the nonlinear group delay model. The ANGDME introduces a complex Bayesian compressive sensing (CBCS) framework to process the sparse reconstruction. Then, a hierarchical Laplace scale mixture (LSM) prior is utilized to model dependencies among coefficients and provides superior probabilistic predictions. Furthermore, the estimator of amplitudes and group delays (GDs) of signals are obtained from the posterior distribution by Bayesian inference instead of point estimation. Finally, the proposed method updates the dictionary matrix in a traditional data-driven manner, resulting in a high-resolution time-frequency representation. Both simulated and experimental results illustrate the adaptability and effectiveness of the proposed method.