The total deviation approach to long-term characterization offrequency stability

摘要

Total variance represents the first advancement in the estimationnof an oscillating signal's long-term frequency stability since thenconventional Allan variance estimator. It is called “Totvar”n(pronounced tot-var) for short. Its commonly reported square-root is thentotal deviation function called “Totdev” (tot-dev). Totdevnefficiently extracts broadband FM oscillator noise levels and typesncommonly encountered at long-term Τ-averaging times, even thoughnthese are difficult to measure. The notable advantages of Totdevninclude: significantly improved confidence for estimating long-termnfrequency stability, lower sensitivity to the removal of linearnfrequency drift, and exact decomposition of the sample variance ofnfrequency residuals. A review of some methods of improving thenestimation of long-term stability is presented. Concepts of datanextrapolation and smoothing are developed and linked to the definitionnof Totdev. The approach to interpreting a Σ vs. Τ stabilitynplot of Totdev is given and is identical to that using the Allanndeviation. Formulas are given for computing confidence interval at longnterm and for computing an easily removed, slight negative bias. The lastnsection shows how Totdev is the first frequency-stability statistic thatnis unified to the more readily understood, but often inappropriate,nstandard deviation by an exact decomposition