Nonlinear Filtering of Weak Chaotic Signals

Valeri Kontorovich, Zinaida Lovtchikova and Fernando Ramos-Alarcon

A chapter in Chaos Theory from IntechOpen

Abstract: In recent years, the application of nonlinear filtering for processing chaotic signals has become relevant. A common factor in all nonlinear filtering algorithms is that they operate in an instantaneous fashion, that is, at each cycle, a one moment of time magnitude of the signal of interest is processed. This operation regime yields good performance metrics, in terms of mean squared error (MSE) when the signal-to-noise ratio (SNR) is greater than one and shows moderate degradation for SNR values no smaller than -3 dB. Many practical applications require detection for smaller SNR values (weak signals). This chapter presents the theoretical tools and developments that allow nonlinear filtering of weak chaotic signals, avoiding the degradation of the MSE when the SNR is rather small. The innovation introduced through this approach is that the nonlinear filtering becomes multimoment, that is, the influence of more than one moment of time magnitudes is involved in the processing. Some other approaches are also presented.

Keywords: nonlinear filtering; chaotic systems; Rossler attractor; Lorenz attractor; Chua attractor; Kalman filter; weak signals; mean squared error (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:122365

DOI: 10.5772/intechopen.70717

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