Negative Power Law Noise, Reality vs. Myth
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) alpha |f| p for 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 in a 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2009
- Accession Number
- ADA518075
Entities
People
- Victor S. Reinhardt
Organizations
- RTX