Total Variance as an Exact Analysis of the Sample Variance
Abstract
Given a sequence of fractional frequency deviates, we investigated the relationship between the sample variance of these deviates and the total variance (Totvar) estimator of the Allan variance. We demonstrated that we can recover exactly twice the sample variance by renormalizing the Totvar estimator and then summing it over dyadic averaging times 1, 2, 4, . . . , 2(J) along with one additional term that represents variations at all dyadic averaging times greater than 2(J). This decomposition of the sample variance mimics a similar theoretical decomposition in which summing the true Allan variance over all possible dyadic averaging times yields twice the process variance. We also establish a relationship between the Totvar estimator of the Allan variance and a biased maximal overlap estimator that uses a circularized version of the original fractional frequency deviates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1997
- Accession Number
- ADA512149
Entities
People
- David A. Howe
- Donald B. Percival
Organizations
- University of Washington