Part of the book: Recent Advances in Wireless Communications and Networks
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.
Part of the book: Chaos Theory
This chapter develops and extends the general theoretical results, previously published in the chapter “Nonlinear filtering of weak chaotic signals”, and presents detailed implementations of a computationally simple, robust (filtering fidelity almost insensitive to changes of the desired input signal properties) and rather precise approach for the filtering of weak signals of different physical nature (biological, seismic, voice, etc.) in presence of white Gaussian noise. The implementations rely on non-linear filtering techniques that in general can be considered as either one-moment or multi-moment, in the sense that they operate with a single sample (instantaneous fashion) or with various adjacent samples (non-instantaneous fashion). Chaotic modeling of the real input signals allows achieving an almost ubiquitous filtering approach with a computationally simple implementation. Application of the linearization strategies (for both one and two-moment filtering) provide, additionally, “invariance” of the processing algorithms to variations on the nature and statistics of the input signals.
Part of the book: Research Advances in Chaos Theory