Clustering based multiple state–space projections

The method of Nonlinear State–Space Projections (NSSP) is very effective in suppression of white Gaussian noise; however, in colored noise environment its operation is not satisfactory. In this paper, we propose an idea of multiple weighted state–space projections aimed to increase projective filtering performance in this demanding environment. We introduce a new method of state–space points clustering which combines a linguistically defined initialization of prototypes with possibilistic approach to memberships calculation and prototypes refinement. For each cluster created, a signal subspace is formed, and each state–space point is projected on the assumed number of the selected signal subspaces. Weighting the corrections resulting from such projections, according to the distances between the projected point and the clusters prototypes, allows to limit errors caused by wrong construction of the subspaces involved. Automatic calculation of the subspaces dimensions allows for further improvement of the colored noise suppression. The proposed methods are applied to electrocardiograms (ECG) processing and compared to a few previously developed modifications of nonlinear projective filtering. Tested in the colored electromyographic (EMG) noise environment, they significantly outperform the reference methods. Their possible applications are discussed and an exemplary one, concerning separation of the maternal and the fetal ECG, is illustrated.