Abstract 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.

中文翻译：

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基于聚类的多状态空间投影

摘要 非线性状态空间投影（NSSP）方法对抑制高斯白噪声非常有效；然而，在有色噪声环境中，它的操作并不令人满意。在本文中，我们提出了一种多重加权状态空间投影的想法，旨在提高这种苛刻环境中的投影过滤性能。我们引入了一种新的状态空间点聚类方法，该方法将原型的语言定义初始化与成员资格计算和原型细化的可能性方法相结合。对于创建的每个集群，形成一个信号子空间，并且每个状态空间点被投影到假定数量的选定信号子空间上。根据投影点与集群原型之间的距离，对由此类投影产生的修正进行加权，允许限制由错误构造所涉及的子空间引起的错误。子空间维度的自动计算允许进一步改进有色噪声抑制。所提出的方法应用于心电图 (ECG) 处理，并与一些先前开发的非线性投影滤波修改进行比较。在彩色肌电图 (EMG) 噪声环境中进行测试，它们的性能明显优于参考方法。讨论了它们可能的应用，并举例说明了有关分离母体和胎儿心电图的示例。所提出的方法应用于心电图 (ECG) 处理，并与一些先前开发的非线性投影滤波修改进行比较。在彩色肌电图 (EMG) 噪声环境中进行测试，它们的性能明显优于参考方法。讨论了它们可能的应用，并举例说明了有关分离母体和胎儿心电图的示例。所提出的方法应用于心电图 (ECG) 处理，并与一些先前开发的非线性投影滤波修改进行比较。在彩色肌电图 (EMG) 噪声环境中进行测试，它们的性能明显优于参考方法。讨论了它们可能的应用，并举例说明了有关分离母体和胎儿心电图的示例。