Incremental Sparse Bayesian Learning for Parameter Estimation of Superimposed Signals

This work discuses a novel algorithm for joint sparse estimation of superimposed signals and their parameters. The proposed method is based on two concepts: a variational Bayesian version of the incremental sparse Bayesian learning (SBL)– fast variational SBL – and a variational Bayesian approach for parameter estimation of superimposed signal models. Both schemes estimate the unknown parameters by minimizing the variational lower bound on model evidence; also, these optimizations are performed incrementally with respect to the parameters of a single component. It is demonstrated that these estimations can be naturally unified under the framework of variational Bayesian inference. It allows, on the one hand, for an adaptive dictionary design for FV-SBL schemes, and, on the other hand, for a fast superresolution approach for parameter estimation of superimposed signals. The experimental evidence collected with synthetic data as well as with estimation results for measured multipath channels demonstrate the effectiveness of the proposed algorithm.