The total deviation approach to long-term characterization of frequency stability

Total variance represents the first advancement in the estimation of an oscillating signal's long-term frequency stability since the conventional Allan variance estimator. It is called "Totvar" (pronounced tot-var) for short. Its commonly reported square-root is the total deviation function called "Totdev" (tot-dev). Totdev efficiently extracts broadband FM oscillator noise levels and types commonly encountered at long-term tau-averaging times, even though these are difficult to measure. The notable advantages of Totdev include: significantly improved confidence for estimating long-term frequency stability, lower sensitivity to the removal of linear frequency drift, and exact decomposition of the sample variance of frequency residuals. A review of some methods of improving the estimation of long-term stability is presented. Concepts of data extrapolation and smoothing are developed and linked to the definition of Totdev. The approach to interpreting a sigma vs. tau stability plot of Totdev is given and is identical to that using the Allan deviation. Formulas are given for computing confidence interval at long term and for computing an easily removed, slight negative bias. The last section shows how Totdev is the first frequency-stability statistic that is unified to the more readily understood, but often inappropriate, standard deviation by an exact decomposition.