Adaptive sparse estimation of nonlinear chirp signals using Laplace priors

The identification of nonlinear chirp signals has attracted notable attention in the recent literature, including estimators such as the variational mode decomposition and the nonlinear chirp mode estimator. However, most presented methods fail to process signals with close frequency intervals or depend on user-determined parameters that are often non-trivial to select optimally. In this work, we propose a fully adaptive method, termed the adaptive nonlinear chirp mode estimation. The method decomposes a combined nonlinear chirp signal into its principal modes, accurately representing each mode's time-frequency representation simultaneously. Exploiting the sparsity of the instantaneous amplitudes, the proposed method can produce estimates that are smooth in the sense of being piecewise linear. Furthermore, we analyze the decomposition problem from a Bayesian perspective, using hierarchical Laplace priors to form an efficient implementation, allowing for a fully automatic parameter selection. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm is found to yield reliable estimates even when encountering signals with crossed modes. The method's practical potential is illustrated on a whale whistle signal.