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

Bruce Griffiths bruce.griffiths at xtra.co.nz
Fri Apr 23 04:44:26 EDT 2010


There has been some work done on the effect of finite correlation 
between oscillator outputs.
In some cases allowing a finite correlation coefficient improves the N 
cornered hat ADEV estimates.
In most cases the oscillators being compared share the same ambient 
environment and thus may exhibit correlated fluctaution due to ambient 
paramaeter (temperature, pressure humidity etc) variations.

Bruce

Bob Camp wrote:
> Hi
>
> How to treat a negative is up to you, it's obviously indicating a "not real"
> outcome. Zero is also a "not real" for realizable oscillators. Most simply
> note the result as "below floor", drop it, and proceed.
>
> Since the variability of the data is driving the negative results, it's
> unlikely that another approach will massively improve things (with the same
> data set). The practical answer is to use oscillators with closer noise
> performance to reduce the scatter or to improve the data collection method
> if it's the limiting factor.
>
> Bob
>
> -----Original Message-----
> From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On
> Behalf Of Kyle Wesson
> Sent: Thursday, April 22, 2010 5:07 PM
> To: time-nuts at febo.com
> Subject: [time-nuts] Frequency Stability of An Individual
> Oscillator:Negative Values?
>
> 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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