Negative Power Law Noise, Reality vs. Myth

Victor S. Reinhardt

Abstract:	In this paper, it is shown that two popular conceptions about the behavior of negative power law (neg-p) noise—that is, noise with a PSD Lp(f) ? |f|pfor p < 0—are based on myth and that the reality is quite different. The first myth is that one can “fix” a neg-p divergence problem ina variance like a standard or N-sample variance simply by replacing it with an Allan or Hadamard variance without further action. The paper will show that each type of variance has a different interpretation as an error measure and that such arbitrary swapping merely masks the true problem. In the process, we will show that such variance divergences are true indicators of severe system or modeling problems that must be physically addressed, not ignored. The second myth is that one can use ensemble-based statistical estimation techniques like least squares and Kalman filters to properly estimate polynomial deterministic behavior in data containing non-highpass filtered neg-p noise. It is demonstrated that such noise can generate highly anomalous fitting results because non-highpass-filtered neg-p noise is both infinitely correlated and non-ergodic. Thus, non-p noise is shown to act more like systematic error than conventional noise in such cases.
Published in:	Proceedings of the 41st Annual Precise Time and Time Interval Systems and Applications Meeting November 16 - 19, 2009 Hyatt Regency Tamaya Resort Santa Ana Pueblo, New Mexico
Pages:	131 - 144
Cite this article:	Reinhardt, Victor S., "Negative Power Law Noise, Reality vs. Myth," Proceedings of the 41st Annual Precise Time and Time Interval Systems and Applications Meeting, Santa Ana Pueblo, New Mexico, November 2009, pp. 131-144.
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