# [time-nuts] Frequency Stability of An Individual Oscillator: Negative Values?

Pete Rawson peterawson at earthlink.net
Thu Apr 22 21:37:01 UTC 2010

```Kyle,

I suggest that you contact David Allan directly, via his website, with
this question. Going to the source is most likely to produce a useful

Pete Rawson

On Apr 22, 2010, at 3:07 PM, Kyle Wesson wrote:

> Hello,
>
> I am working to determine the Allan variance of an individual
> oscillator from a series of three paired measurements as described in
> the paper by Gray and Allan "A Method for Estimating the Frequency
> Stability of An Individual Oscillator" (NIST, 1974,
> tf.nist.gov/general/pdf/57.pdf). In this report they make reference to
> the statistical uncertainty of the measurement due to ensemble noise
> and potential clock phase correlation which can potentially make the
> Allan variance for an individual oscillator have a negative value.
> They write:
>
> "If the noise level of the oscillator being measured is low enough,
> and the scatter high enough, equation (4) may occasionally give a
> negative value for the variance."
>
> My question is: how should I treat negative variance values in this
> case? For example, if my data set were to produce an individual
> oscillator Allan variance with a value of -5e-12, should I convert
> this value to 0 (ie. the closest valid sigma value to the number since
> 0 <= sigma < inf ), take the absolute value of the result (ie. turn
> -5e-12 to +5e-12), or drop the result from my estimate of individual
> oscillator frequency stability altogether?
>
> Is there another method that will produce estimates of individual
> oscillators from an ensemble approach but assures non-negative output
> variances?
>
> Thank you in advance,
> Kyle
>
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```