A Non Probabilistic Algorithm Based on Karhunen-Loÿve Transform for the Recognition of Stochastic Signals

This paper proposes an efficient methodology that is able to accurately recognize nondeterministic signals generated by stochastic processes (SPs). This technique is based on (i) a training algorithm, which iteratively extracts suitable parameter collections; (ii) a recognition procedure that measures the trajectory-proximities by means of an ad-hoc metric, in order to associate the unknown signal to an SP by using a representation based on Karhunen-Loeve transform (KLT). The recognition algorithm exploits a modelling of several signal classes based on KLT, inasmuch this representation effectively characterizes projections of every SP signal in terms of nondeterministic trajectories defined on associated spaces. The methodology is able to recognize SPs without probability density function (pdf) estimation, and with low-computational complexity: exhaustive experimentations on specific case-studies have shown high recognition performance. As application examples, SPs generated by stochastic nonlinear-differential-equations (SNDEs), with different initial conditions and coefficients being random variables (RVs), have been considered