Robust filtering of weak signals from real phenomena

Main Article Content

Fernando Ramos-Alarcon
Valeri Kontorovich


In a large number of real-life scenarios it is required to process desired signals that are significantly immersed into background noise: tectonic signals from the entrails of the earth, signals coming from the far away cosmos, biometric telemetry signals, distant acoustic signals, noninvasive neural interfaces and so on. The purpose of this paper is to present the description of a robust and efficient platform for the real time filtering of signals deeply immersed in noise (rather weak signals) with rather different nature. The proposed strategy is based on two principles: the chaotic modelling of the signals describing the physical phenomena and the application of filtering strategies based on the theory of non-linear dynamical systems. Considering as a study case seismic signals, fetal electrocardiogram signals, voice-like signals and radio frequency interference signals, this experimental work shows that the proposed methodology is efficient (with mean squared error values less than 1%) and robust (the filtering structure remains the same although the phenomenological signals are drastically different). It turns out that the presented methodology is very attractive for the real time detection of weak signals in practical applications because it offers a high filtering precision with a minimum computational complexity and short processing times.
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[1] Y. Li, B. Yang, Y. Yuan, X. Zhao, and H. Lin, “Ability to detect weak effective seismic signals by utilizing chaotic vibrator system,” Chinese Science Bulletin, vol. 51, pp. 3010–3017, 2006. [Online]. Available:
[2] Y. Li, B. J. Yang, J. Badal, X. P. Zhao, H. B. Lin, and R. L. Li, “Chaotic system detection of weak seismic signals,” Geophysical Journal International, vol. 178, no. 3, pp. 1493–1522, 2009. [Online]. Available:
[3] J. Shu-Yao, Y. Fei, C. Ke-Yu, and C. En, “Application of stochastic resonance technology in underwater acoustic weak signal detection,” in OCEANS 2016 - Shanghai, April 2016, pp. 1–5. [Online]. Available:
[4] S. L. Joshi, R. A. Vatti, and R. V. Tornekar, “A survey on ecg signal denoising techniques,” in 2013 International Conference on Communication Systems and Network Technologies, April 2013, pp. 60–64. [Online]. Available:
[5] H. Li, R. Wang, S. Cao, Y. Chen, N. Tian, and X. Chen, “Weak signal detection using multiscale morphology in microseismic monitoring,” Journal of Applied Geophysics, vol. 133, pp. 39–49, 2016. [Online]. Available:
[6] R. Han, J. Li, G. Cui, X. Wang, W. Wang, and X. Li, “Seismic signal detection algorithm based on gs transform filtering and emd denoising,” in 2018 IEEE 4th International Conference on Computer and Communications (ICCC), Dec 2018, pp. 1213–1217. [Online]. Available:
[7] H. Van Trees, Detection, Estimation, and Modulation Theory: Detection, Estimation, and Linear Modulation Theory, 2001. [Online]. Available:
[8] A. Jazwinski, Stochastic Processes and Filtering Theory. Academic Press, 1970. [Online]. Available:
[9] R. L. Stratonovich, Topics of the Theory of Random Noise, 1967. [Online]. Available:
[10] W.-R. Wu and A. Kundu, “Image estimation using fast modified reduced update kalman filter,” IEEE Transactions on Signal Processing, vol. 40, no. 4, pp. 915–926, April 1992. [Online]. Available:
[11] R. Parseh, K. Kansanen, and D. Slock, “Distortion outage analysis for joint space-time coding and kalman filtering,” IEEE Transactions on Signal Processing, vol. 65, no. 9, pp. 2291–2305, May 2017. [Online]. Available:
[12] M. de Sousa Vieira, “Chaos and synchronized chaos in an earthquake model,” Kontorovich y Ramos-Alarcón / Filtraje robusto de señales débiles de fenómenos reales 119 Physical Review Letters, vol. 82, pp. 201– 204, Jan 1999. [Online]. Available:
[13] G. Kolumban, M. P. Kennedy, and L. O. Chua, “The role of synchronization in digital communications using chaos. i . fundamentals of digital communications,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 10, pp. 927–936, Oct 1997. [Online]. Available:
[14] G. Kaddoum, “Design and performance analysis of a multiuser ofdm based differential chaos shift keying communication system,” IEEE Transactions on Communications, vol. 64, no. 1, pp. 249–260, Jan 2016. [Online]. Available:
[15] N. V. Thakor, “Chaos in the heart: signals and models,” in Proceedings of the 1998 2nd International Conference Biomedical Engineering Days, May 1998, pp. 11–18. [Online]. Available:
[16] P. J. García-Laencina and G. Rodríguez-Bermudez, “Analysis of eeg signals using nonlinear dynamics and chaos: A review,” Applied Mathematics & Information Sciences, pp. 2309–2321, 2015. [Online]. Available:
[17] V. S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, and L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems. Springer-Verlag Berlin Heidelberg, 2007. [Online]. Available:
[18] V. Kontorovich and Z. Lovtchikova, “Nonlinear filtering of chaos for real time applications,” in Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering, K. Kyamakya, W. A. Halang, W. Mathis, J. C. Chedjou, and Z. Li, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 41–59. [Online]. Available:
[19] V. Kontorovich, Z. Lovtchikova, and F. Ramos-Alarcon, Nonlinear Filtering of Weak Chaotic Signals, 2017. [Online]. Available:
[20] E. Nikulchev, “Simulation of robust chaotic signal with given properties,” Advanced Studies in Theoretical Physics, vol. 8, no. 21, pp. 939–944, 2014. [Online]. Available:
[21] L. Ljung, System Identification: Theory for the user. Prentice Hall PTR, 1999. [Online]. Available:
[22] V. Pugachev and I. Sinitsyn, Stochastic Differential systems Analysis and Filtering. John Wiley & Sons, 1987. [Online]. Available:
[23] M. Banbrook, S. McLaughlin, and I. Mann, “Speech characterization and synthesis by nonlinear methods,” IEEE Transactions on Speech and Audio Processing, vol. 7, no. 1, pp. 1–17, Jan 1999. [Online]. Available:
[24] D. Ilitzky Arditti, A. Alcocer Ochoa, V. Kontorovich Mazover, and F. Ramos Alarcon Barroso, “Adaptive mitigation of platformgenerated radio-frequency interference,” Patent US 2015.0 051 880A1, 2015. [Online]. Available:
[25] Physionet. (2019) Physiobank atm. [Online]. Available:
[26] F. R. Rofooei, A. Mobarake, and G. Ahmadi, “Generation of artificial earthquake records with a nonstationary kanai-tajimi model,” Engineering Structures, vol. 23, no. 7, pp. 827–837, 2001. [Online]. Available:
[27] E. X. Alban, M. E. Magana, H. G. Skinner, and K. P. Slattery, “Statistical modeling of the interference noise generated by computing platforms,” IEEE Transactions on Electromagnetic Compatibility, vol. 54, no. 3, pp. 574–584, June 2012. [Online]. Available: