Calculate Theoretical Allan Variance for Stationary First-Order Autoregressive (AR1) Process

Source: R/ANVS.R

This function allows us to calculate the theoretical allan variance for stationary first-order autoregressive (AR1) process.

av_ar1(n, phi, sigma2)

Arguments

n

An integer value for the size of the cluster.
phi

A double value for the autocorrection parameter \(\phi\).
sigma2

A double value for the variance parameter \(\sigma ^2\).

Value

A double indicating the theoretical allan variance for AR1 process.

Note

This function is based on the calculation of the theoretical allan variance for stationary AR1 process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang.) This calculation is fundamental and necessary for the study in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al. (IEEE Signal Processing Letters, 2017).

Examples

av1 = av_ar1(n = 5, phi = 0.9, sigma2 = 1)
av2 = av_ar1(n = 8, phi = 0.5, sigma2 = 2)