Robust Coherent Noise Suppression by Point Estimation of the Cauchy Location Parameter

This paper introduces a new point estimation algorithm, with particular focus on coherent noise suppression, given several measurements of the device under test where it is assumed that 1) the noise is first-order stationery and 2) the device under test is linear and time-invariant. The algorithm exploits the robustness of the Pitman estimator of the Cauchy location parameter through the initial scaling of the test signal by a centred Gaussian variable of predetermined variance. It is illustrated through mathematical derivations and simulation results that the proposed algorithm is more accurate and consistently robust to outliers for different tailed density functions than the conventional methods of sample mean (coherent averaging technique) and sample median search.

• Ephraim Gower
• Thato Tsalaile
• Monageng Kgwadi
• Malcolm Hawksford.

• Central limit theorem
• Fisher-Cramer Rao
• gamma function
• Pitman estimator.

<p>[1] O. Rompelman and H. H. Ros, “Coherent averaging technique: A tutorial
review Part 1: Noise reduction and the equivalent filter,” Journal of
Biomedical Engineering. vol. 8, pp. 24-29, 1986.
[2] O. Rompelman and H. H. Ros, “Coherent averaging technique: A tutorial
review Part 2: Trigger jitter, overlapping responses and non-periodic
stimulation,” Journal of Biomedical Engineering., vol. 8, pp. 30-35, 1986.
[3] R. L. Fincham, “Refinements in the Impulse Testing of Loudspeakers?,”
Journal of Audio Engineering Society., vol.33, pp. 133-140, 1985.
[4] M. Sherman, “Comparing the Sample Mean and the Sample Median: An
Exploration in the Exponential Power Family,” The American Statistician.,
vol. 1, pp. 52-54, 1997.
[5] W. Feller, An Introduction to Probability Theory and its Applications, 3rd
edition,New York: Wiley, 1971.
[6] K. W. Ng, Q. H. Tang and H. Yang, “Maxima of Sums of Heavy-tailed
Random Variables,” Austin Bulletin, vol. 32, pp. 43-55, 2002.
[7] G. B. Freue, “The Pitman estimator of the Cauchy location parameter,”
Journal of Statistical Planning and Inference., vol.137, pp. 1900-1913,
2007.
[8] S. C. Port and C. J. Stone, “Fisher Information and the Pitman Estimator
of a Location Parameter,” Annals of Statistics., vol. 2, pp. 225-247, 1974.
[9] J. H. Curtiss, “On the Distribution of the Quotient of Two Chance
Variabless,” Annals of Mathematical Statistics., vol. 12, pp. 409-421,
1941.</p>