Package 'avar'

Title:	Allan Variance
Description:	Implements the allan variance and allan variance linear regression estimator for latent time series models. More details about the method can be found, for example, in Guerrier, S., Molinari, R., & Stebler, Y. (2016) <doi:10.1109/LSP.2016.2541867>.
Authors:	Stéphane Guerrier [aut, cre], James Balamuta [aut], Gaetan Bakalli [aut], Roberto Molinari [aut], Justin Lee [aut], Ahmed Radi [aut], Haotian Xu [aut], Yuming Zhang [aut], Nathanael Claussen [aut], Lionel Voirol [ctb]
Maintainer:	Stéphane Guerrier <[email protected]>
License:	AGPL-3
Version:	0.1.2
Built:	2024-10-29 04:47:05 UTC
Source:	https://github.com/smac-group/avar

Help Index

Allan variance of IMU Data from an ADIS 16405 sensor
Calculate Theoretical Allan Variance for Stationary First-Order Autoregressive (AR1) Process
Calculate Theoretical Allan Variance for Drift Process
Calculate Theoretical Allan Variance for Stationary Quantization Noise Process
Calculate Theoretical Allan Variance for Random Walk Process
Calculate Theoretical Allan Variance for Stationary White Noise Process
Computes the Allan Variance Linear Regression estimator
Calculate Theoretical Covariance Matrix of AR(1) Blocks Process
Calculate Theoretical Covariance Matrix of Bias-Instability Process
Calculate Theoretical Covariance Matrix of Non-Stationary White Noise Process
Internal function to the Allan Variance Linear Regression estimator
Allan variance of IMU Data from IMAR Gyroscopes
Allan variance of IMU Data from a KVH1750 IMU sensor
Allan variance of IMU Data from a LN200 sensor
Non-stationary Maximal-overlapping Allan Variance
Allan variance of IMU Data from a navchip sensor
Non-stationary Non-overlapping Allan Variance
Plot Allan Deviation
Plot the AVLR with the Allan Variance
Plot Allan Variance based on IMU Data
Plot the AVLR with the Allan Deviation for IMU
Prints Allan Variance
Summary Allan Variance

Allan variance of IMU Data from an ADIS 16405 sensor

Description

This data set contains Allan variance of gyroscope and accelerometer data from an ADIS 16405 sensor.

Usage

adis_av
adis_av

Format

A list of the following elements:

"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.

Source

The IMU data comes from Department of Geomatics Engineering, University of Calgary.

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

Description

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

Usage

av_ar1(n, phi, sigma2)
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, 2008, Metrologia, 45(5): 549. 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., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Author(s)

Yuming Zhang

Examples

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

Calculate Theoretical Allan Variance for Drift Process

Description

This function allows us to calculate the theoretical allan variance for drift process.

Usage

av_dr(delta, n)
av_dr(delta, n)

Arguments

`delta`	A `double` value for the noise parameter $\delta$ .
`n`	An `integer` value for the size of the cluster.

Value

A double indicating the theoretical allan variance for the drift process.

Note

This function is based on the calculation of the theoretical allan variance for drift process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang, 2008, Metrologia, 45(5): 549. 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., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Examples

av1 = av_dr(delta = 1, n = 5)
av2 = av_dr(delta = 2, n = 8)
av1 = av_dr(delta = 1, n = 5)
av2 = av_dr(delta = 2, n = 8)

Calculate Theoretical Allan Variance for Stationary Quantization Noise Process

Description

This function allows us to calculate the theoretical allan variance for stationary quantization noise process.

Usage

av_qn(Q2, n)
av_qn(Q2, n)

Arguments

`Q2`	A `double` value for the noise parameter $Q^2$ .
`n`	An `integer` value for the size of the cluster.

Value

A double indicating the theoretical allan variance for the quantization noise process.

Note

This function is based on the calculation of the theoretical allan variance for stationary quantization noise process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang, 2008, Metrologia, 45(5): 549. 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., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Examples

av1 = av_qn(Q2 = 1, n = 5)
av2 = av_qn(Q2 = 2, n = 8)
av1 = av_qn(Q2 = 1, n = 5)
av2 = av_qn(Q2 = 2, n = 8)

Calculate Theoretical Allan Variance for Random Walk Process

Description

This function allows us to calculate the theoretical allan variance for random walk process.

Usage

av_rw(omega2, n)
av_rw(omega2, n)

Arguments

`omega2`	A `double` value for the noise parameter $\omega ^2$ .
`n`	An `integer` value for the size of the cluster.

Value

A double indicating the theoretical allan variance for the random walk process.

Note

This function is based on the calculation of the theoretical allan variance for random walk process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang, 2008, Metrologia, 45(5): 549. 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., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Examples

av1 = av_rw(omega2 = 1, n = 5)
av2 = av_rw(omega2 = 2, n = 8)
av1 = av_rw(omega2 = 1, n = 5)
av2 = av_rw(omega2 = 2, n = 8)

Calculate Theoretical Allan Variance for Stationary White Noise Process

Description

This function allows us to calculate the theoretical allan variance for stationary white noise process.

Usage

av_wn(sigma2, n)
av_wn(sigma2, n)

Arguments

`sigma2`	A `double` value for the variance parameter $\sigma ^2$ .
`n`	An `integer` value for the size of the cluster.

Value

A double indicating the theoretical allan variance for the white noise process.

Note

This function is based on the calculation of the theoretical allan variance for stationary white noise process raised in "Allan Variance of Time Series Models for Measurement Data" by Nien Fan Zhang, 2008, Metrologia, 45(5): 549. 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., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Examples

av1 = av_wn(sigma2 = 1, n = 5)
av2 = av_wn(sigma2 = 2, n = 8)
av1 = av_wn(sigma2 = 1, n = 5)
av2 = av_wn(sigma2 = 2, n = 8)

Computes the Allan Variance Linear Regression estimator

Description

Estimate the parameters of time series models based on the Allan Variance Linear Regression (AVLR) approach

Usage

avlr(x, ...)

## Default S3 method:
avlr(
  x,
  qn = NULL,
  wn = NULL,
  rw = NULL,
  dr = NULL,
  ci = FALSE,
  B = 100,
  alpha = 0.05,
  ...
)

## S3 method for class 'imu_avar'
avlr(
  x,
  qn_gyro = NULL,
  wn_gyro = NULL,
  rw_gyro = NULL,
  dr_gyro = NULL,
  qn_acc = NULL,
  wn_acc = NULL,
  rw_acc = NULL,
  dr_acc = NULL,
  B = 100,
  alpha = 0.05,
  ...
)
avlr(x, ...)

## Default S3 method:
avlr(
  x,
  qn = NULL,
  wn = NULL,
  rw = NULL,
  dr = NULL,
  ci = FALSE,
  B = 100,
  alpha = 0.05,
  ...
)

## S3 method for class 'imu_avar'
avlr(
  x,
  qn_gyro = NULL,
  wn_gyro = NULL,
  rw_gyro = NULL,
  dr_gyro = NULL,
  qn_acc = NULL,
  wn_acc = NULL,
  rw_acc = NULL,
  dr_acc = NULL,
  B = 100,
  alpha = 0.05,
  ...
)

Arguments

`x`	A `vec` of time series observations or an `imu` object.
`...`	Further arguments passed to other methods.
`qn`	A `vec` specifying on which scales the parameters of a Quantization Noise (QN) should be computed.
`wn`	A `vec` specifying on which scales the parameters of a White Noise (WN) should be computed.
`rw`	A `vec` specifying on which scales the parameters of a Random Wakk (RW) should be computed.
`dr`	A `vec` specifying on which scales the parameters of a Drift (DR) should be computed.
`ci`	A `boolean` to compute parameter confidence intervals.
`B`	A `double` for the number of bootstrap replicates to compute the parameter confidence intervals.
`alpha`	A `double` defining the level of the confidence interval (1 - 'alpha').
`qn_gyro`	A `vec` specifying on which scales the parameters of a Quantization Noise (QN) should be computed for the gyroscope component.
`wn_gyro`	A `vec` specifying on which scales the parameters of a White Noise (WN) should be computed for the gyroscope component.
`rw_gyro`	A `vec` specifying on which scales the parameters of a Random Wakk (RW) should be computed for the gyroscope component.
`dr_gyro`	A `vec` specifying on which scales the parameters of a Drift (DR) should be computed for the gyroscope component.
`qn_acc`	A `vec` specifying on which scales the parameters of a Quantization Noise (QN) should be computed for the accelerometer component.
`wn_acc`	A `vec` specifying on which scales the parameters of a White Noise (WN) should be computed for the accelerometer component.
`rw_acc`	A `vec` specifying on which scales the parameters of a Random Wakk (RW) should be computed for the accelerometer component.
`dr_acc`	A `vec` specifying on which scales the parameters of a Drift (DR) should be computed for the accelerometer component.

Value

If the input x is a vec, then the function returns a list that contains:

"estimates": The estimated value of the parameters.
"implied_ad": The Allan deviation implied by the estimated parameters.
"implied_ad_decomp": The Allan deviation implied by the estimated parameters for each individual model (if more than one is specified).
"av": The avar object computed from the provided data.

If the input x is of the class imu_avar, then the function returns a list that contains:

"gyro": The estimation results correseponding to the gyroscope component.
"acc": The estimation results correseponding to the accelerometer component.
"imu_av": The imu_avar object computed based on the IMU data.

Examples


set.seed(999)

N = 100000
Xt = rnorm(N) + cumsum(rnorm(N, 0, 3e-3))

av = avar(Xt)
plot(av)

# Input time series
fit = avlr(Xt, wn = 1:8, rw = 11:15)
fit

# Input directly Allan variance
fit = avlr(av, wn = 1:8, rw = 11:15)
fit

# Plot functions
plot(fit)
plot(fit, decomp = TRUE)
plot(fit, decomp = TRUE, show_scales = TRUE)

set.seed(999)

N = 100000
Xt = rnorm(N) + cumsum(rnorm(N, 0, 3e-3))

av = avar(Xt)
plot(av)

# Input time series
fit = avlr(Xt, wn = 1:8, rw = 11:15)
fit

# Input directly Allan variance
fit = avlr(av, wn = 1:8, rw = 11:15)
fit

# Plot functions
plot(fit)
plot(fit, decomp = TRUE)
plot(fit, decomp = TRUE, show_scales = TRUE)

Calculate Theoretical Covariance Matrix of AR(1) Blocks Process

Description

This function allows us to calculate the theoretical covariance matrix of a non-stationary AR(1) blocks process.

Usage

covmat_ar1blocks(n_total, n_block, phi, sigma2)
covmat_ar1blocks(n_total, n_block, phi, sigma2)

Arguments

`n_total`	An `integer` indicating the length of the whole AR(1) blocks process.
`n_block`	An `integer` indicating the length of each block of the AR(1) blocks process.
`phi`	A `double` value for the autocorrection parameter $\phi$ .
`sigma2`	A `double` value for the variance parameter $\sigma ^2$ .

Value

The theoretical covariance matrix of the AR(1) blocks process.

Note

This function helps calculate the theoretical covariance matrix of a non-stationary process, AR(1) blocks. It is helpful to calculate the theoretical allan variance of non-stationary processes, which can be used to compare with the theoretical allan variance of stationary processes as shown in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Author(s)

Yuming Zhang

Examples

covmat1 = covmat_ar1blocks(n_total = 1000, n_block = 10,
phi = 0.9, sigma2 = 1)
covmat2 = covmat_ar1blocks(n_total = 800, n_block = 20,
phi = 0.5, sigma2 = 2)
covmat1 = covmat_ar1blocks(n_total = 1000, n_block = 10,
phi = 0.9, sigma2 = 1)
covmat2 = covmat_ar1blocks(n_total = 800, n_block = 20,
phi = 0.5, sigma2 = 2)

Calculate Theoretical Covariance Matrix of Bias-Instability Process

Description

This function allows us to calculate the theoretical covariance matrix of a bias-instability process.

Usage

covmat_bi(sigma2, n_total, n_block)
covmat_bi(sigma2, n_total, n_block)

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.

Value

The theoretical covariance matrix of the bias-instability process.

Note

This function helps calculate the theoretical covariance matrix of a non-stationary process, bias-instability. It is helpful to calculate the theoretical allan variance of non-stationary processes, which can be used to compare with the theoretical allan variance of stationary processes as shown in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Author(s)

Yuming Zhang

Examples

covmat1 = covmat_bi(sigma2 = 1, n_total = 1000, n_block = 10)
covmat2 = covmat_bi(sigma2 = 2, n_total = 800, n_block = 20)
covmat1 = covmat_bi(sigma2 = 1, n_total = 1000, n_block = 10)
covmat2 = covmat_bi(sigma2 = 2, n_total = 800, n_block = 20)

Calculate Theoretical Covariance Matrix of Non-Stationary White Noise Process

Description

This function allows us to calculate the theoretical covariance matrix of a non-stationary white noise process.

Usage

covmat_nswn(sigma2, n_total)
covmat_nswn(sigma2, n_total)

Arguments

`sigma2`	A `double` value for the variance parameter $\sigma ^2$ .
`n_total`	An `integer` indicating the length of the whole non-stationary white noise process.

Value

The theoretical covariance matrix of the non-stationary white noise process.

Note

This function helps calculate the theoretical covariance matrix of a non-stationary process, non-stationary white noise. It is helpful to calculate the theoretical allan variance of non-stationary processes, which can be used to compare with the theoretical allan variance of stationary processes as shown in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Author(s)

Yuming Zhang

Examples

covmat1 = covmat_nswn(sigma2 = 1, n_total = 1000)
covmat2 = covmat_nswn(sigma2 = 2, n_total = 800)
covmat1 = covmat_nswn(sigma2 = 1, n_total = 1000)
covmat2 = covmat_nswn(sigma2 = 2, n_total = 800)

Internal function to the Allan Variance Linear Regression estimator

Description

Estimate the parameters of time series models based on the Allan Variance Linear Regression (AVLR) approach

Usage

fit_avlr(qn, wn, rw, dr, ad, scales)
fit_avlr(qn, wn, rw, dr, ad, scales)

Arguments

`qn`	A `vec` specifying on which scales the parameters of a Quantization Noise (QN) should be computed.
`wn`	A `vec` specifying on which scales the parameters of a White Noise (WN) should be computed.
`rw`	A `vec` specifying on which scales the parameters of a Random Wakk (RW) should be computed.
`dr`	A `vec` specifying on which scales the parameters of a Drift (DR) should be computed.
`ad`	A `vec` of the Allan variance.
`scales`	A `vec` of the scales.

Value

A list with the estimated parameters.

Allan variance of IMU Data from IMAR Gyroscopes

Description

This data set contains Allan variance of IMAR gyroscopes data.

Usage

imar_av
imar_av

Format

A list of the following elements:

"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.

Source

The IMU data comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

Allan variance of IMU Data from a KVH1750 IMU sensor

Description

This data set contains Allan variance of gyroscope and accelerometer data from an KVH1750 sensor.

Usage

kvh1750_av
kvh1750_av

Format

A list of the following elements:

"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.

Source

The IMU data comes from Department of Geomatics Engineering, University of Calgary.

Allan variance of IMU Data from a LN200 sensor

Description

This data set contains Allan variance of LN200 gyroscope and accelerometer data.

Usage

ln200_av
ln200_av

Format

A list of the following elements:

"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.

Source

The IMU data comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

Non-stationary Maximal-overlapping Allan Variance

Description

Calculation of the theoretical Maximal-overlapping Allan variance for constant-mean non-stationary time series data.

Usage

MOAV(n, covmat)
MOAV(n, covmat)

Arguments

`n`	An `integer` indicating the length of each vector of consecutive observations considered for the average.
`covmat`	A `matrix` indicating the T-by-T covariance matrix of the time series with length T.

Details

This calculation of Maximal-overlapping Allan variance is based on the definition on "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260. Here n is an integer larger than 1 and smaller than $floor\left(log_2 \left(dim\left(covmat\right)[1]\right)\right)-1$ .

Value

A field <numeric> that is the theoretical Maximal-overlapping Allan variance for constant-mean non-stationary time series data.

Author(s)

Haotian Xu

Examples


set.seed(999)
Xt = arima.sim(n = 100, list(ar = 0.3))
avar(Xt, type = "to")

a = matrix(rep(0, 1000^2), nrow = 1000)
for (i in 1:1000){
  a[,i] = seq(from = 1 - i, length.out = 1000)
}
a.diag = diag(a)
a[upper.tri(a,diag=TRUE)] = 0
a = a + t(a) + diag(a.diag)
covmat = 0.3^a
sapply(1:8, function(y){MOAV(2^y, covmat)})

set.seed(999)
Xt = arima.sim(n = 100, list(ar = 0.3))
avar(Xt, type = "to")

a = matrix(rep(0, 1000^2), nrow = 1000)
for (i in 1:1000){
  a[,i] = seq(from = 1 - i, length.out = 1000)
}
a.diag = diag(a)
a[upper.tri(a,diag=TRUE)] = 0
a = a + t(a) + diag(a.diag)
covmat = 0.3^a
sapply(1:8, function(y){MOAV(2^y, covmat)})

Allan variance of IMU Data from a navchip sensor

Description

This data set contains Allan variance of gyroscope and accelerometer data from a navchip sensor.

Usage

navchip_av
navchip_av

Format

A list of the following elements:

"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.

Source

The IMU data of the navchip sensor comes from Geodetic Engineering Laboratory (TOPO) and Swiss Federal Institute of Technology Lausanne (EPFL).

Non-stationary Non-overlapping Allan Variance

Description

Calculation of the theoretical Non-overlapping Allan variance for constant-mean non-stationary time series data.

Usage

NOAV(n, covmat)
NOAV(n, covmat)

Arguments

`n`	An `integer` indicating the length of each vector of consecutive observations considered for the average.
`covmat`	A `matrix` indicating the T-by-T covariance matrix of the time series with length T.

Details

This calculation of Non-overlapping Allan variance is based on the definition on "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260. Here n is an integer larger than 1 and smaller than $floor\left(log_2 \left(dim\left(covmat\right)[1]\right)\right)-1$ .

Value

A field <numeric> that is the theoretical Non-overlapping Allan variance for constant-mean non-stationary time series data.

Author(s)

Haotian Xu

Examples


set.seed(999)
Xt = arima.sim(n = 100, list(ar = 0.3))
avar(Xt, type = "to")

a = matrix(rep(0, 1000^2), nrow = 1000)
for (i in 1:1000){
  a[,i] = seq(from = 1 - i, length.out = 1000)
}
a.diag = diag(a)
a[upper.tri(a,diag=TRUE)] = 0
a = a + t(a) + diag(a.diag)
covmat = 0.3^a
sapply(1:8, function(y){NOAV(2^y, covmat)})


set.seed(999)
Xt = arima.sim(n = 100, list(ar = 0.3))
avar(Xt, type = "to")

a = matrix(rep(0, 1000^2), nrow = 1000)
for (i in 1:1000){
  a[,i] = seq(from = 1 - i, length.out = 1000)
}
a.diag = diag(a)
a[upper.tri(a,diag=TRUE)] = 0
a = a + t(a) + diag(a.diag)
covmat = 0.3^a
sapply(1:8, function(y){NOAV(2^y, covmat)})

Plot Allan Deviation

Description

Displays a plot of Allan variance with its corresponding pointwise confidence intervals.

Usage

## S3 method for class 'avar'
plot(
  x,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ci_ad = NULL,
  point_cex = NULL,
  point_pch = NULL,
  text_legend_cex = 1,
  ...
)
## S3 method for class 'avar'
plot(
  x,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ci_ad = NULL,
  point_cex = NULL,
  point_pch = NULL,
  text_legend_cex = 1,
  ...
)

Arguments

`x`	An `avar` object.
`units`	A `string` that specifies the units of time plotted on the x axis.
`xlab`	A `string` that gives a title for the x axis.
`ylab`	A `string` that gives a title for the y axis.
`main`	A `string` that gives an overall title for the plot.
`col_ad`	A `string` that specifies the color of the line allan variance line.
`col_ci`	A `string` that specifies the color of the shaded area covered by the confidence intervals.
`nb_ticks_x`	An `integer` that specifies the maximum number of ticks for the x-axis.
`nb_ticks_y`	An `integer` that specifies the maximum number of ticks for the y-axis.
`legend_position`	A `string` that specifies the position of the legend (use `legend_position = NA` to remove legend).
`ci_ad`	A `boolean` that determines whether to plot the confidence interval shaded area.
`point_cex`	A `double` that specifies the size of each symbol to be plotted.
`point_pch`	A `double` that specifies the symbol type to be plotted.
`text_legend_cex`	A `double` that specifies the size of the legend text.
`...`	Additional arguments affecting the plot.

Value

A plot of the Allan deviation and relative confidence interval for each scale.

Author(s)

Stephane Guerrier, Nathanael Claussen and Justin Lee

Examples


set.seed(999)
Xt = rnorm(10000)
av = avar(Xt)

plot(av)
plot(av, main = "Simulated white noise", xlab = "Scales")
plot(av, units = "sec", legend_position = "topright")
plot(av, col_ad = "darkred", col_ci = "pink")

set.seed(999)
Xt = rnorm(10000)
av = avar(Xt)

plot(av)
plot(av, main = "Simulated white noise", xlab = "Scales")
plot(av, units = "sec", legend_position = "topright")
plot(av, col_ad = "darkred", col_ci = "pink")

Plot the AVLR with the Allan Variance

Description

Displays a plot of the Allan variance (AV) with the CI values and the AV implied by the estimated parameters.

Usage

## S3 method for class 'avlr'
plot(
  x,
  decomp = FALSE,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ci_ad = NULL,
  point_cex = NULL,
  point_pch = NULL,
  show_scales = FALSE,
  text_legend_cex = 1,
  ...
)
## S3 method for class 'avlr'
plot(
  x,
  decomp = FALSE,
  units = NULL,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  legend_position = NULL,
  ci_ad = NULL,
  point_cex = NULL,
  point_pch = NULL,
  show_scales = FALSE,
  text_legend_cex = 1,
  ...
)

Arguments

`x`	An `avlr` object.
`decomp`	A `boolean` that determines whether the contributions of each individual model are plotted.
`units`	A `string` that specifies the units of time plotted on the x axis.
`xlab`	A `string` that gives a title for the x axis.
`ylab`	A `string` that gives a title for the y axis.
`main`	A `string` that gives an overall title for the plot.
`col_ad`	A `string` that specifies the color of the line allan variance line.
`col_ci`	A `string` that specifies the color of the shaded area covered by the confidence intervals.
`nb_ticks_x`	An `integer` that specifies the maximum number of ticks for the x-axis.
`nb_ticks_y`	An `integer` that specifies the maximum number of ticks for the y-axis.
`legend_position`	A `string` that specifies the position of the legend (use `legend_position = NA` to remove legend).
`ci_ad`	A `boolean` that determines whether to plot the confidence interval shaded area.
`point_cex`	A `double` that specifies the size of each symbol to be plotted.
`point_pch`	A `double` that specifies the symbol type to be plotted.
`show_scales`	A `boolean` that specifies if the scales used for each process should be plotted.
`text_legend_cex`	A `double` that specifies the size of the legend text.
`...`	Additional arguments affecting the plot.

Value

Plot of Allan deviation and relative confidence intervals for each scale.

Author(s)

Stephane Guerrier and Justin Lee

Examples


set.seed(999)

N = 100000
Xt = rnorm(N) + cumsum(rnorm(N, 0, 3e-3))
av = avlr(Xt, wn = 1:7, rw = 12:15)

plot.avlr(av)
plot.avlr(av, decomp = TRUE, main = "Simulated white noise", xlab = "Scales")
plot.avlr(av, units = "sec", legend_position = "topright")
plot.avlr(av, col_ad = "darkred", col_ci = "pink")
plot.avlr(av, decomp = TRUE, show_scales = TRUE)

set.seed(999)

N = 100000
Xt = rnorm(N) + cumsum(rnorm(N, 0, 3e-3))
av = avlr(Xt, wn = 1:7, rw = 12:15)

plot.avlr(av)
plot.avlr(av, decomp = TRUE, main = "Simulated white noise", xlab = "Scales")
plot.avlr(av, units = "sec", legend_position = "topright")
plot.avlr(av, col_ad = "darkred", col_ci = "pink")
plot.avlr(av, decomp = TRUE, show_scales = TRUE)

Plot Allan Variance based on IMU Data

Description

Displays a plot of Allan variance based on IMU data with its corresponding pointwise confidence intervals.

Usage

## S3 method for class 'imu_avar'
plot(
  x,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  ci_ad = NULL,
  point_pch = NULL,
  point_cex = NULL,
  ...
)
## S3 method for class 'imu_avar'
plot(
  x,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  ci_ad = NULL,
  point_pch = NULL,
  point_cex = NULL,
  ...
)

Arguments

`x`	An `avar` object.
`xlab`	A `string` that gives a title for the x axis.
`ylab`	A `string` that gives a title for the y axis.
`main`	A `string` that gives an overall title for the plot.
`col_ad`	A `string` that specifies the color of the line allan variance line.
`col_ci`	A `string` that specifies the color of the shaded area covered by the confidence intervals.
`nb_ticks_x`	An `integer` that specifies the maximum number of ticks for the x-axis.
`nb_ticks_y`	An `integer` that specifies the maximum number of ticks for the y-axis.
`ci_ad`	A `boolean` that determines whether to plot the confidence interval shaded area.
`point_pch`	A `double` that specifies the symbol type to be plotted.
`point_cex`	A `double` that specifies the size of each symbol to be plotted.
`...`	Additional arguments affecting the plot.

Value

A plot of the Allan deviation and relative confidence interval for each scale.

Author(s)

Stephane Guerrier and Yuming Zhang

Examples

data("navchip_av")
plot(navchip_av)
data("navchip_av")
plot(navchip_av)

Plot the AVLR with the Allan Deviation for IMU

Description

Displays a plot of the Allan variance (AV) with the CI values and the AV implied by the estimated parameters for the IMU.

Usage

## S3 method for class 'imu_avlr'
plot(
  x,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  ci_ad = NULL,
  point_pch = NULL,
  point_cex = NULL,
  ...
)
## S3 method for class 'imu_avlr'
plot(
  x,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  col_ad = NULL,
  col_ci = NULL,
  nb_ticks_x = NULL,
  nb_ticks_y = NULL,
  ci_ad = NULL,
  point_pch = NULL,
  point_cex = NULL,
  ...
)

Arguments

`x`	An `avlr` object.
`xlab`	A `string` that gives a title for the x axis.
`ylab`	A `string` that gives a title for the y axis.
`main`	A `string` that gives an overall title for the plot.
`col_ad`	A `string` that specifies the color of the line allan variance line.
`col_ci`	A `string` that specifies the color of the shaded area covered by the confidence intervals.
`nb_ticks_x`	An `integer` that specifies the maximum number of ticks for the x-axis.
`nb_ticks_y`	An `integer` that specifies the maximum number of ticks for the y-axis.
`ci_ad`	A `boolean` that determines whether to plot the confidence interval shaded area.
`point_pch`	A `double` that specifies the symbol type to be plotted.
`point_cex`	A `double` that specifies the size of each symbol to be plotted.
`...`	Additional arguments affecting the plot.

Value

Plot of Allan deviation and relative confidence intervals for each scale.

Author(s)

Stephane Guerrier and Justin Lee

Examples


data(navchip_av)
navchip_avlr = avlr(navchip_av, wn_gyro = 1:20, rw_gyro = 1:20, wn_acc = 1:20, rw_acc = 1:20)
plot(navchip_avlr)

data(navchip_av)
navchip_avlr = avlr(navchip_av, wn_gyro = 1:20, rw_gyro = 1:20, wn_acc = 1:20, rw_acc = 1:20)
plot(navchip_avlr)

Prints Allan Variance

Description

Displays the information on the output of the 'avar()' function

Usage

## S3 method for class 'avar'
print(x, ...)
## S3 method for class 'avar'
print(x, ...)

Arguments

`x`	A `avar` object.
`...`	Arguments to be passed to methods

Value

console output

Examples

set.seed(999)
Xt = rnorm(10000)
out = avar(Xt)
print(out)

set.seed(999)
Xt = rnorm(10000)
out = avar(Xt)
print(out)

Summary Allan Variance

Description

Displays the summary table of the output of the 'avar()' function

Usage

## S3 method for class 'avar'
summary(object, ...)
## S3 method for class 'avar'
summary(object, ...)

Arguments

object

A avar object.

...

Additional arguments affecting the summary produced. A table that contains:

"Time": The averaging time at each level.
"AVar": The estimated Allan variance.
"ADev": The estimated Allan deviation.
"Lower CI": The lower bound of the confidence interval for the Allan deviation (ADev).
"Upper CI": The upper bound of the confidence interval for the Allan deviation (ADev).

Examples

set.seed(999)
Xt = rnorm(10000)
out = avar(Xt)
summary(out)

set.seed(999)
Xt = rnorm(10000)
out = avar(Xt)
summary(out)