Analysis of meridian estimator performance for non-Gaussian PDF data samples
D.A. Kurkin, A.A. Roenko, & V.V. Lukin
National Aerospace University,
17, Chkalova Str., Kharkiv, 61070, Ukraine Address all correspondence to V.V. Lukin E-mail: lukin@ai.kharkov.com
I. Djurovic
University of Montenegro,
Cetinsky put bb, 81000, Podgorica, Montenegro
Abstract
A sample meridian estimator of location parameter (LP) has been proposed recently and shown to be robust and controllable by means of a tunable parameter . The estimator properties have been initially studied but not analyzed thoroughly. In this paper we address several practical questions. First, we analyze conditions under which statistical properties of meridian estimator of LP considerably differ from those ones of the sample median estimator. Second, we give examples of probability density functions for which the sample meridian estimates can be sufficiently more accurate than sample median. Third, we consider practical situations when useful properties of the meridian estimator of LP can be exploited in practice of signal and data processing.
KEY WORDS: signal processing, estimator, location parameters, noise
References
- Spaulding, A.D. and Middleton, D., (1977), Optimum reception in an impulsive interference environment. Part I: Coherent Detection. IEEE Trans. Commun. 25(9):910-923.
- Huber, P., (1981), Robust statistics, Wiley, New York.
- Astola, J. and Kuosmanen, P., (1997), Fundamentals of nonlinear digital filtering, Boca Raton (USA), CRC Press LLC, - 276 ð.
- Kalluri, S. and Arce, G., (1998), Adaptive Weighted Myriad Filter Algorithms for Robust Signal Processing in a-stable Noise Environments, IEEE Trans. on Signal Processing, 46(2):322-334.
- Djurovic, I. and Lukin, V., (2006), Robust DFT with high breakdown point for complex valued impulse noise environment, IEEE Signal Processing Letters, 13(1):25-28.
- Lukin, V.V., Abramov, S.K., Zelensky, A.A., and Astola, J.T., (2005), Myriad based shift parameter estimation method and its application to image filtering and processing, Proceedings of SPIE Conference “Mathematical Methods in Pattern and Image Analysis”, San Diego (USA), July-Aug. 2005, 5916:1-12.
- Taguchi, A., (1994), Adaptive α-Trimmed Mean Filter with Excellent-Detail Preserving, Proceedings of ICASSP, pp. 61-64.
- Lim Heng Siong, Chuah Teong Chee, and Chuah Hean Teik, (2007), On the Optimal Alpha-k Curve of the Sample Myriad, IEEE Signal Processing Letters, 14(8):545-548.
- Aysal, T.C. and Barner, K.E., (2007), Meridian Filtering for Robust Signal Processing, IEEE Transactions on Signal Processing, 55(8):3949-3962.
- Huang, T.S., (ed.) (1981), Two-Dimensional Digital Signal Processing II. Transforms and Median Filters. Springer-Verlag.
- Lukin, V., Totsky, A., Fevralev, D., Roenko, A., Astola, J., and Egiazarian, K., (2006), Adaptive Combined Bispectrum-Filtering Signal Processing in Radar Systems with Low SNR, Proceedings of ISCAS, Kos Island, Greece, pp. 3690-3693.
- Katkovnik, V., (1999), Robust M-estimates of the frequency and amplitude of a complex-valued harmonic, Signal Processing, 77:71-84.
- Roenko, A., Lukin, V., Djurovic, I., and Abramov, S., (2008), Adaptation of Sample Myriad Tunable Parameter to Characteristics of SaS Distribution, Proceedings of the Conference on Mathematical Methods in Electromagnetic Theory (MMET 2008), Odessa, Ukraine, pp. 418-420.
- Suoranta, R., (1995), Amplitude domain approach to digital filtering. Theory and applications, Thesis for the degree of Doctor of Technology, Tampere, Finland, - 199 p.
- Aysal, T.C. and Barner, K.E., (2006), Second-Order Heavy-Tailed Distributions and Tail Analysis, IEEE Trans. on Signal Processing, 54(7):2827-2832.
|