avari: Allan Variance (from integrated values).
In allanvar: Allan Variance Analysis

Description Usage Arguments Details Value Author(s) References Examples

The function avari computes the Allan Variance of a set of values with a given constant sampling frequency. The diferent with avar function is that the input values are the integral value of sensor output (i.e: rate/acceleration). That means angle from gyros and velocity from accelerometers. In this version of the Allan variance computation the number and size of cluster n has been computed as in avar function n=2^l, l=1,2,…(Allan 1987).

1	avari(values, freq)

`values`	Integration of the calibrated sensor output (i.e: angel or velocity)
`freq`	Sampling frequency rate in Hertz

The Allan variance can also be defined either in terms of the output rate as defined in avar by Ω(t) or using the output angle/velocity as this function does. Defining:

θ(t) = \int^t Ω(t^{'})dt^{'}

The lower integration limit is not specified as only angle differences are employed in the definition. Angle measurement are made at discrete times given by t = nt_0, n = 1,2,…, N. The notation is simplify by writing θ_k = θ (k t_0). The cluster average is now defined as:

\bar{Ω}_k(τ)= (θ_{k+n} - θ_k)/τ and \bar{Ω}_{k+1}(τ)= (θ_{k+2n} - θ_{k+n})/(τ)

The equivalent Allan Variance estimation is defined as:

θ^2(τ) = 1/(2τ^2 (N - 2n)) ∑_{k=1}^{N-2n} [θ_{k+2n} - 2θ_{k+n} + θ_k ]^2

Return an object of class data.frame containing the Allan Variance computation with the following fields:

`time`	Value of the cluster time.
`av`	The Allan variance value: variance among clusters of same size.
`error`	Error on the estimation: Uncertainty of the value.

Javier Hidalgo Carrio <javier.hidalgo_carrio@dfki.de>

Allan, D. W. (1966) Statistics of Atomic Frequency Standards Proceedings of IEEE, vol. 54, no. 2, pp. 221-230, Feb, 1966.

IEEE Std 952-1997 IEEE Standard Specification Format Guide and Test Procedure for Single Axis Interferometric Fiber Optic Gyros.

El-Sheimy, N.; Haiying Hou.; Xiaoji, Niu (2008) Analysis and Modeling of Inertial Sensors Using Allan Variance IEEE Transaction on Instrumentation and Measurement.

#Load data 
data(gyroz)

#Allan variance computation using avari
#Simple integration of the angular velocity
igyroz <- cumsum(gyroz@.Data * (1/frequency(gyroz)))
igyroz <- ts (igyroz, start=c(igyroz[1]), delta=(1/frequency(gyroz)))
avigyroz <- avari(igyroz@.Data, frequency(igyroz))
plotav(avigyroz)
abline(1.0+log(avigyroz$time[1]), -1/2, col="green", lwd=4, lty=10)
abline(1.0+log(avigyroz$time[1]), 1/2, col="green", lwd=4, lty=10)
legend(0.11, 1e-03, c("Random Walk"))
legend(25, 1e-03, c("Rate Random Walk"))