Allan variance is used to measure the frequency stability of oscillation for a sequence of data in the time domain. It can also be used to determine the intrinsic noise in a system as a function of the averaging time. The averaging time series τ can be specified as τ = m/fs. Here fs is the sampling frequency of data, and m is a list of ascending averaging factors (such as 1, 2, 4, 8, …).
returns the Allan variance
tau] = allanvar(
avar as a function of averaging time
tau. The default averaging time
tau is an octave
sequence given as (1, 2, ...,
where N is the number of samples in
Omega is specified as a matrix,
over the columns of
Determine Allan Variance of Single Axis Gyroscope
Load gyroscope data from a MAT file, including the sample rate of the data in Hz. Calculate the Allan variance.
load('LoggedSingleAxisGyroscope','omega','Fs') [avar,tau] = allanvar(omega,'octave',Fs);
Plot the Allan variance on a
loglog(tau,avar) xlabel('\tau') ylabel('\sigma^2(\tau)') title('Allan Variance') grid on
Determine Allan Deviation at Specific Values of
Generate sample gyroscope noise, including angle random walk and rate random walk.
numSamples = 1e6; Fs = 100; nStd = 1e-3; kStd = 1e-7; nNoise = nStd.*randn(numSamples,1); kNoise = kStd.*cumsum(randn(numSamples,1)); omega = nNoise+kNoise;
Calculate the Allan deviation at specific values of . The Allan deviation is the square root of the Allan variance.
m = 2.^(9:18); [avar,tau] = allanvar(omega,m,Fs); adev = sqrt(avar);
Plot the Allan deviation on a
loglog(tau,adev) xlabel('\tau') ylabel('\sigma(\tau)') title('Allan Deviation') grid on
Omega — Input data
N-by-1 vector | N-by-M matrix
Input data specified as an N-by-1 vector or an
N-by-M matrix. N is the
number of samples, and M is the number of sample sets. If specified
as a matrix,
allanvar operates over the columns of
m — Averaging factor
scalar | vector
Averaging factor, specified as a scalar or vector with ascending integer values less
than (N-1)/2, where N is the number of samples in
ptStr — Point specification of
'octave' (default) |
fs — Basic frequency of input data in Hz
Basic frequency of the input data,
Omega, in Hz, specified as
a positive scalar.
avar — Allan variance of input data
vector | matrix
Allan variance of input data at
tau, returned as a vector or
tau — Averaging time of Allan variance
vector | matrix
Averaging time of Allan variance, returned as a vector, or a matrix.
Introduced in R2019a