V. F. Borulko, S. M. Vovk


Myriad filtering and meridian filtering are known as robust methods of signal processing. The theory of these methods is based on the
generalized Cauchy distribution and maximum-likelihood criterion. Based on the “Principle of Minimum Duration”, we present an alternative
approach to justify and generalize the myriad and meridian filtering methods. The proposed approach shows that the myriad and
meridian filtering methods are special cases of the minimum-duration filtering methods derived from a concept of “signal quasi-duration”.
Mathematically, this concept is implemented through the concept of a functional (i.e., a function of a function) by using the proposed set
of cost functions. On this foundation, a “superfamily” of quasi-duration functional is built, and a general class of minimum-duration filtering
methods which depends on the three free-adjustable parameters is introduced. The numerical simulations are performed to compare the
proposed and conventional methods for the problem of filtering a constant signal which is distorted by a mixture of Cauchy, Laplacian and
Gaussian noise.


myriad filtering, meridian filtering, duration


Gonzalez J. G. Optimality of the myriad filter in practical impulsivenoise environments / J. G. Gonzalez, G. R. Arce // IEEE Trans. on Signal Processing. – 2001. – Vol. 49, No. 2. – P. 438–441. 2. Nunez R. C. Fast and accurate computation of the myriad filter via branch-and-bound search / R. C. Nunez, J. G. Gonzalez, G. R. Arce // IEEE Trans. Signal Processing. – 2008. – Vol. 56, No. 7. – P. 3340–3346. 3. Aysal T. C. Meridian filtering for robust signal processing / T. C. Aysal, K. E. Barner // IEEE Trans. on Signal Processing. – 2007. – Vol. 55, No. 8. – P. 3949–3962. 4. Analysis of meridian estimator performance for non-Gaussian PDF data samples / [D. A. Kurkin, V. V. Lukin, A. A. Roenko, I. Djurovic] // Telecommunications and Radio Engineering. – 2010. – Vol. 69, No. 8. – P. 669–679. 5. Huber P. J. Robust estimation of a location parameter / P. J. Huber // Annals of Mathematical Statistics. – 1964. – Vol. 35, No. 1. – P. 73–101. 6. Huber P. J. Robust statistics / P. J. Huber. – New York : John Wiley and Sons, 1981. – 312 p. 7. Carrillo R. E. Generalized Cauchy distribution based robust estimation / R. E. Carrillo, T. C. Aysal, K. E. Barner // Acoustic, Speech and Signal Processing : IEEE International Conference ICASSP 2008, Las Vegas, 31 March – 4 April 2008 : proceedings. – IEEE, 2008. – P. 3389–3392. DOI: 10.1109/ICASSP.2008.4518378 8. Vovk S. M. A minimum-duration method for recovering finite signals / S. M. Vovk, V. F. Borul’ko // Radioelectronics and Communications Systems. – 1991. – Vol. 34. – P. 67–69. 9. Vovk S. M. Elimination of the measurement background by the minimum duration method / S. M. Vovk, V. F. Borulko // Radioelectronics and Communications Systems. – 1998. – Vol. 41. – P. 48–49. 10. Vovk S. M. Statement of a problem of definition of linear signals parameters in quasinormed space / S. M. Vovk, V. F. Borul’ko // Radioelectronics and Communications Systems. – 2010. – Vol. 53. – P. 367–375.

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