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This paper proposes a method for modeling and analyzing the stability of a solution to the inverse problem of extracting individual signals from an additive mixture of several signals that come to measurement points from various signal sources inaccessible for direct measurement. Stability analysis is accomplished by determining those intervals (singular intervals) for parameters of a signal formation model in which steady signal separation is achievable. We have developed algorithms to calculate singular intervals for different parameter variations of a signal formation model—absolute, relative, critical, and their combinations—that simulate various practically significant types of model parameter perturbations that affect the stability of the solution to this inverse problem. The paper also presents the results of computer modeling for the proposed algorithms.

Modeling and investigating the stability of a solution to the inverse problem of signal separation