gen_bi: Generate Bias-Instability Process

Description Usage Arguments Value Note Author(s) Examples

View source: R/avns.R

Description

This function allows us to generate a non-stationary bias-instability process.

Usage

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gen_bi(sigma2, n_total, n_block, title = NULL, seed = 135, ...)

Arguments

sigma2

A double value for the variance parameter sigma^2.

n_total

An integer indicating the length of the whole bias-instability process.

n_block

An integer indicating the length of each block of the bias-instability process.

title

A string of the time series data name.

seed

An integer set for simulation replication purpose.

...

Additional parameters.

Value

A vector containing the bias-instability process.

Note

This function helps generate a non-stationary process example, bias-instability, whose theoretical maximum overlapping allan variance (MOAV) is close to the theoretical MOAV of its closest stationary AR(1) process over some scales. However, this approximation is not good enough when considering the logarithmic representation of the allan variance. Therefore, the exact form of the allan variance of this non-stationary process allows us to better interpret the signals characterized by bias-instability, as shown in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al. (IEEE Signal Processing Letters, 2017), preprint available: https://arxiv.org/abs/1702.07795.

Author(s)

Yuming Zhang

Examples

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Xt = gen_bi(sigma2 = 1, n_total = 1000, n_block = 10)
plot(Xt)

Yt = gen_bi(sigma2 = 0.8, n_total = 800, n_block = 20,
title = "non-stationary bias-instability process")
plot(Yt)

SMAC-Group/simts documentation built on Feb. 21, 2018, 3:34 p.m.