Unsupervised feature extraction, signal labeling, and blind signal separation in a state space world

The paper addresses the problem of joint signal separation and estimation in a single-channel discrete-time signal composed of a wandering baseline and overlapping repetitions of unknown (or known) signal shapes. All signals are represented by a linear state space model (LSSM). The baseline model is driven by white Gaussian noise, but the other signal models are triggered by sparse inputs. Sparsity is achieved by normal priors with unknown variance (NUV) from sparse Bayesian learning. All signals and system parameters are jointly estimated with an efficient expectation maximization (EM) algorithm based on Gaussian message passing, which works both for known and unknown signal shapes. The proposed method outputs a sparse multi-channel representation of the given signal, which can be interpreted as a signal labeling.