avar | R Documentation |
This function estimates the Allan variance.
avar(x, type = "mo", ...)
## Default S3 method:
avar(x, type = "mo", freq = 1, ...)
## S3 method for class 'imu'
avar(x, type = "mo", ...)
x |
A |
type |
A |
... |
Further arguments passed to other methods. |
The decomposition and the amount of time it takes to perform this function depends on whether you are using the Maximal Overlap or the Tau Overlap.
If the input x
is a vec
, then the function returns a list
that contains:
"levels": The averaging time at each level.
"allan": The estimated Allan variance.
"type": Type of estimator (mo
or to
).
If the input x
is an imu
object, then the function returns a list
that contains:
"sensor": Name of the sensor.
"freq": The frequency at which the error signal is measured.
"n": Sample size of the data.
"type": The types of sensors considered in the data.
"axis": The axes of sensors considered in the data.
"avar": A list containing the computed Allan variance based on the data.
Given N
equally spaced samples with averaging time \tau = n\tau _0
,
we define n
as an integer such that 1 \le n \le \frac{N}{2}
.
Therefore, n
can be selected from \left\{ {n|n < \left\lfloor {{{\log }_2}\left( N \right)} \right\rfloor } \right\}
Based on the latter, we have M = N - 2n
levels of decomposition.
The Maximal-overlap estimator is given by:
\frac{1}{{2\left( {N - 2k + 1} \right)}}\sum\limits_{t = 2k}^N {{{\left[ {{{\bar Y}_t}\left( k \right) - {{\bar Y}_{t - k}}\left( k \right)} \right]}^2}}
where
{{\bar y}_t}\left( \tau \right) = \frac{1}{\tau }\sum\limits_{i = 0}^{\tau - 1} {{{\bar y}_{t - i}}}
.
Given N
equally spaced samples with averaging time \tau = n\tau _0
,
we define n
as an integer such that 1 \le n \le \frac{N}{2}
.
Therefore, n
can be selected from \left\{ {n|n < \left\lfloor {{{\log }_2}\left( N \right)} \right\rfloor } \right\}
Based on the latter, we have m = \left\lfloor {\frac{{N - 1}}{n}} \right\rfloor - 1
levels of decomposition.
The tau-overlap estimator is given by:
where {{\bar y}_t}\left( \tau \right) = \frac{1}{\tau }\sum\limits_{i = 0}^{\tau - 1} {{{\bar y}_{t - i}}}
.
Long-Memory Processes, the Allan Variance and Wavelets, D. B. Percival and P. Guttorp
set.seed(999)
Xt = rnorm(10000)
av_mat_mo = avar(Xt, type = "mo", freq = 100)
av_mat_tau = avar(Xt, type = "to")
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