Windowed State-Space Filters for Signal Detection and Separation

This paper introduces a toolbox for model-based detection, separation, and reconstruction of signals that is especially suited for biomedical signals, such as electrocardiograms (ECGs) or electromyograms (EMGs). The modeling is based on autonomous linear state space models (LSSMs), which are localized with flexible windows. The models are fit to observations by minimizing the squared error while the use of LSSMs leads to efficient recursive error computations and minimizations. Multisection windows enable complex models, and per-sample weights enable multistage processing or adaptive smoothing. This paper is motivated by, and intended for, practical applications, for which several examples and tabulated cost computations are given.