How to compute Allan Variance without allanvar?

Hi,

I would like to compute the Allan Variance to study a signal but without the existing Matlab function. Actually I wanted to see how matlab computes it but we don't have access to it (*.p file, btw I wonder why this function is not accessible?).

Actually I have a good article ( Techniques Ingénieur, VERNOTTE, R681) Stabilité temporelle et fréquentielle des oscillateurs : outils d’analyse that gives all the basics to compute by hand the Allan Variance.

I tried to reproduce the result displayed at the allanvar matlab page but I didn't manage. I don't have the trend as the figure displayed. Can anyone take a look at my code? Maybe i mistyped the formula? My function is:

function out = AllanVar(sig,n,dt)
    y1  = sum(sig(1:1+n));
    y2  = sum(sig(2:2+n));
    out = (y2-y1)^2/2/(n*dt)^2;
end

And to remove the noise we can average it over multiple draws with:

numSamples = 1e6;
Pow         = nextpow2(numSamples)-1;
N           = 100;
m           = 2.^(1:Pow);
aVar        = zeros(N,length(m));
for k = 1:N
    Fs          = 100;
    nStd        = 1e-3;
    kStd        = 1e-7;
    nNoise      = nStd.*randn(numSamples,1);
    kNoise      = kStd.*cumsum(randn(numSamples,1));
    omega       = nNoise+kNoise;
    
    for j = 1:length(m)
        aVar(k,j) = AllanVar(omega,m(j),1/Fs);
    end
end

tau = m*dt;

figure
loglog(tau,sqrt(mean(aVar)),'k')

But I get a straight line only...

Attached an output figure. Thanks in advance! :)

Answer 1

[Gokul Nath S J]

Hi Louis,

I understood that the allanvariance file is in .p format and you don't have access to it. However, there is a MATALB Exchange file for computing allan deviation which is defined as,

So part from the square root step, rest of the calcuation remains the same.

Kindly find the attachement MATALB Exchange document for more information.

https://www.mathworks.com/matlabcentral/fileexchange/13246-allan.

Thanks,

Gokul Nath S J