animalTrack (version 1.0.0)

accuracy: Estimate accuracy of three axis accelerometer/magnetometer.

Description

The accuracy of the accelerometer and magnetometer is crucial to estimating pitch, roll, and heading. The axes must be orthogonal.

Usage

accuracy(x, y, z)
accuracy.improve(x, y, z)

Arguments

x

a numeric vector of x-axis values.

y

a numeric vector of y-axis values.

z

a numeric vector of z-axis values.

Value

accuracy(), a list containing the raw accuracy values (which should equal 1, in the case of perfect accuracy), variance, and standard deviation

acc

vector containing the estimated accuracy values

var

variance of acc

std

standard deviation of acc

For accuracy.improve(), a list containing multiple components

z.est

vector of estimated Z-axis values.

z.resid

vector of residuals (z - z.est).

acc.input

vector of accuracy values of the input (i.e. vector norm of x, y, z). Same as accuracy().

acc.input.var

accuracy variance of the input values.

acc.input.std

accuracy standard deviation of the input values.

acc.improve

vector of accuracy values using z.est. Same as accuracy(x, y, z.est)

acc.improve.var

accuracy variance of acc.improve.

acc.improve.std

accuracy standard deviation of acc.improve.

Details

In the case of a three-axis accelerometer, the combined static acceleration (i.e. acceleration due to gravity) should always be 1g. Accelerometers measure the Earth's gravity as well as movement of the animal in gravitational units, denoted as g units. The sensor should be calibrated so that 1g = -9.8 $m/s^2$, which is the acceleration due to gravity (this varies locally). The combined acceleration will vary from 1g during dynamic acceleration (e.g. an animal accelerates to chase prey), or if the axes are not perfectly orthogonal. In the case of dynamic acceleration, an effort must be made to filter out the high frequency signal so that only the static signal (i.e. body orientation) remains. The accuracy function evaluates the accuracy of the accelerometer by calculating the vector norm of the acceleration, $A$, using the equation

$A = \sqrt{Ax^2 + Ay^2 + Az^2}$

and subsequently calculating the variance and standard deviation.

The accuracy.improve function provides an estimate of the Z-axis value of the accelerometer using the X and Y-axis values. The Z-axis estimate gives a value for Z that makes the vector norm 1boldg (i.e. all three axes are perfectly orthogonal and X and Y are assumed to be correct). This estimate for Z can then be used to evaluate error that may correspond to pitch angle, or may be a constant error. This will vary between sensors.

References

Grygorenko, V. (2011), Sensing - magnetic compass with tilt compensation. Cypress Perform, AN2272, Document No. 001-32379 Rev. B.

Tuck, K. (2007), Tilt sensing using linear accelerometers. Freescale Semiconductor, AN3461 Rev. 2.

Examples

## Load seal dive data. see help(hugh) for details on variables.
## There are six dives, with surface intervals. here, we will
## look at the first 3 dives.
data(hugh)
## accuracy of the accelerometer.
A.acc.1 <- accuracy(hugh$Ax.dec[hugh$diven == 1],hugh$Ay.dec[hugh$diven == 1],
                    hugh$Az.dec[hugh$diven == 1])
A.acc.2 <- accuracy(hugh$Ax.dec[hugh$diven == 2],hugh$Ay.dec[hugh$diven == 2],
                    hugh$Az.dec[hugh$diven == 2])
A.acc.3 <- accuracy(hugh$Ax.dec[hugh$diven == 3],hugh$Ay.dec[hugh$diven == 3],
                    hugh$Az.dec[hugh$diven == 3])
## Plot the accuracy during the track.
## dive 1 has a high error due to some outliers. dive 2 looks much better.
## dive 3 has some outliers similar to dive 1.
plot(A.acc.1$acc)
plot(A.acc.2$acc)
plot(A.acc.3$acc)
## error angle in degrees
asin(A.acc.1$std)*(180/pi)
asin(A.acc.2$std)*(180/pi)
asin(A.acc.3$std)*(180/pi)

## See if there is a systematic error in the Z-axis. Warnings will occur
## if there are errors in the X, Y, or Z-axis (i.e. too large/small
## of a value). 
acc.d1 <- accuracy.improve(hugh$Ax.dec[hugh$diven == 1],hugh$Ay.dec[hugh$diven == 1],
                           hugh$Az.dec[hugh$diven == 1])
acc.d2 <- accuracy.improve(hugh$Ax.dec[hugh$diven == 2],hugh$Ay.dec[hugh$diven == 2],
                           hugh$Az.dec[hugh$diven == 2])
acc.d3 <- accuracy.improve(hugh$Ax.dec[hugh$diven == 3],hugh$Ay.dec[hugh$diven == 3],
                           hugh$Az.dec[hugh$diven == 3])
## Plot the Z-axis values, the estimates, and the residuals
## We can see that there are large spikes. These spikes may
## coincide with movement. The Z values during these spikes
## could be filtered out, or a new filter to the Z accelerometer
## may be needed. This will vary according to the sensor,
## type of animal, etc.
plot(hugh$Az.dec[hugh$diven == 1],ylim=c(-.5,1.5))
points(acc.d1$z.est,col='red')
lines(acc.d1$z.resid,col='blue')
legend(400,-.05,legend=c("Z-axis","Z-axis estimates","Residuals"),
       lty=c(0,0,1),pch=c(1,1,NA),col=c("black","red","blue"),bty="n")
plot(hugh$Az.dec[hugh$diven == 2],ylim=c(-.5,1.5))
points(acc.d2$z.est,col='red')
lines(acc.d2$z.resid,col='blue')
legend(300,-.05,legend=c("Z-axis","Z-axis estimates","Residuals"),
       lty=c(0,0,1),pch=c(1,1,NA),col=c("black","red","blue"),bty="n")
plot(hugh$Az.dec[hugh$diven == 3],ylim=c(-.5,1.5))
points(acc.d3$z.est,col='red')
lines(acc.d3$z.resid,col='blue')
legend(400,-.05,legend=c("Z-axis","Z-axis estimates","Residuals"),
       lty=c(0,0,1),pch=c(1,1,NA),col=c("black","red","blue"),bty="n")