avar_to_cpp | R Documentation |
Computation of Tau-Overlap Allan Variance
avar_to_cpp(x)
x |
A |
Given N
equally spaced samples with averaging time \tau = n\tau _0
,
where n
is an integer such that 1 \le n \le \frac{N}{2}
.
Therefore, n
is able to be selected from \left\{ {n|n < \left\lfloor {{{\log }_2}\left( N \right)} \right\rfloor } \right\}
Then, a sampling of m = \left\lfloor {\frac{{N - 1}}{n}} \right\rfloor - 1
samples exist.
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}}}
.
av A matrix
that contains:
Col 1The size of the cluster
Col 2The Allan variance
Col 3The error associated with the variance estimation.
JJB
Long-Memory Processes, the Allan Variance and Wavelets, D. B. Percival and P. Guttorp
set.seed(999)
N = 100000
white.noise = rnorm(N, 0, 2)
random.walk = cumsum(0.1*rnorm(N, 0, 2))
combined.ts = white.noise+random.walk
av_mat = avar_to_cpp(combined.ts)
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