Correlation Properties of Chaos: Cumulant Approach

Kontorovich, Valeri; Lovtchikova, Z.; Ramos-Alarcon, F.

doi:10.3390/mca15050946

Cited by 4 publications

(21 citation statements)

References 9 publications

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“…Substituting (2.7) in (2.6) and assuming that h 2 < 1 one can get approximately that normalized 11 κ has the same order as h 2 , i.e. 11 κ~ O(h 2 ).…”

Section: X(t) Is a Chaotic Signal And N(t) Is Awgnmentioning

confidence: 95%

“…Then, let us say that one would like to "correct" the stationary value 2 κ (calculated for the 1MM case) by means of its implicit dependence on 11 κ as if it was "calculated" for the 2MM case.…”

Section: X(t) Is a Chaotic Signal And N(t) Is Awgnmentioning

confidence: 99%

“…Taking into account the complexity limits and that the covariance function of the chaos initially drops rather fast (see [11]), let us take first n = 2 (2MM case).…”

Section: Complementary Theoretical Backgroundmentioning

confidence: 99%

“…In recent years chaotic signals have became the corner stone in many science and engineering fields [8][9][10][11] and have practical applications either in communications, physics or even in biology [12]. Although the filtering for chaotic signals has received considerable attention from researches, practical specialists and academics (see [12][13][14][15][16], just to mention some of the numerous examples) some of the main problems related to real time applications of non-linear algorithms are still not solved.…”

Section: Introductionmentioning

confidence: 99%

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Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Ramos-Alarcon

Kontorovich

2014

2014 11th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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This paper presents experimental results related to the multi-moment non-linear filtering of chaotic signals. For simplicity of implementation only the particular case of two moments filtering (2MM) is developed here. The 2MM filtering approach is specially suited for estimation of extremely weak chaotic signals immersed on an accompanying noise signal (Additive White Gaussian Noise, AWGN) or together with some other type of information signal. The performance of the 2MM technique is rather efficient in the sense that very small values of the Normalized Mean Square Error (NMSE) can be achieved for Chaos/Noise or Chaos/signal ratios below 0 dB. This experimental study allows establishing clearly the trends of the multi-moment approach.

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“…Substituting (2.7) in (2.6) and assuming that h 2 < 1 one can get approximately that normalized 11 κ has the same order as h 2 , i.e. 11 κ~ O(h 2 ).…”

Section: X(t) Is a Chaotic Signal And N(t) Is Awgnmentioning

confidence: 95%

Section: X(t) Is a Chaotic Signal And N(t) Is Awgnmentioning

confidence: 99%

“…Taking into account the complexity limits and that the covariance function of the chaos initially drops rather fast (see [11]), let us take first n = 2 (2MM case).…”

Section: Complementary Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Ramos-Alarcon

Kontorovich

2014

2014 11th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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“…For example, if for one-moment case the MSE , 0.1 percent can be achieved for SNR , 0.5, then for two-moment case it is possible to expect the same MSE with almost 30 percent less SNR. Theoretically, it shows that MSE can be done close to zero for very low SNR levels if chaos can be estimated for very close time instants t 1 and t 2 (Kontorovich et al, 2010a).…”

Section: Nonlinear Filtering Of Chaosmentioning

confidence: 96%

Multi‐moment statistical characterization and nonlinear filtering of chaos

Kontorovich¹,

Lovtchikova²

2013

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -The purpose of this paper is to provide the results of investigation of multi-moment statistical characteristics of chaos and apply them to improve the accuracy of nonlinear algorithms for chaos filtering for real-time applications. Design/methodology/approach -The approach to find multi-moment statistical properties of chaos-multi-moment cumulant (covariance) functions of higher order is a generalization of the previously proposed (by the authors) "degenerated cumulant equations" method. Those multi-moment cumulants functions are applied in the generalization of the Stratonovich-Kushner equations (SKE) for the optimum algorithm of nonlinear filtering of chaos as well as for synthesis of the quasi-optimum algorithms. Findings -Results are presented to investigate the multi-moment statistical properties of chaos and formulate the theoretical background for synthesis of multi-moment optimum and quasi-optimum algorithms for nonlinear filtering of chaos with the improved accuracy in the presence of additive white noise. Originality/value -The paper presents new theoretical results of the statistical description of chaos, previously partially reported only from experimental studies. A novel approach for chaos filtering is also presented. The proposed approach is dedicated to further improvement of the filtering accuracy for the case of low (less than one) SNR scenarios and is important for implementation in real-time processing. As an important practical example, the new modified EKF algorithm is proposed with the rather opportunistic characteristics of the filtering fidelity together with algorithm complexitypractically the same as the "classic" one-moment EKF algorithm.

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“Multi-moment” nonlinear filtering of chaos

Kontorovich

Lovtchikova

2011

Proceedings of the Joint INDS'11 &Amp; ISTET'11

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It was shown in earlier works of the authors that approximate nonlinear filtering algorithms for chaos demonstrate very good filtering accuracy in low SNR scenarios. This paper is the sequel of the research related to statistical properties of chaotic signals and approximate nonlinear filtering algorithms of chaos. In this paper a novel filtering approach is presented; the proposed approach is called as "multi-moment" for the following improvement of the filtering accuracy for low SNR. The general way for synthesis of the optimum and quasi-optimum filtering algorithms based on the criteria of maximum a-posteriori probability is presented, and in the following it is called as modified Stratonovich-Kushner equations (SKE) for a-posteriori Probability Density Function (PDF) and a-posteriori characteristic function. Equations for a-posteriori cumulants are presented hereafter as well and based on those equations was developed the modified EKF algorithm, based on twomoment statistics. The later demonstrates rather opportunistic characteristics for filtering accuracy practically with the same algorithm complexity as the classic EKF

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Correlation Properties of Chaos: Cumulant Approach

Cited by 4 publications

References 9 publications

Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Multi‐moment statistical characterization and nonlinear filtering of chaos

“Multi-moment” nonlinear filtering of chaos

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Correlation Properties of Chaos: Cumulant Approach

Cited by 4 publications

References 9 publications

Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Efficient multi-moment non-linear filtering: Experimental study for low power chaotic signals

Multi‐moment statistical characterization and nonlinear filtering of chaos

&#x201C;Multi-moment&#x201D; nonlinear filtering of chaos

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“Multi-moment” nonlinear filtering of chaos