Technical Explanation – Animal Orientation

Theoretical description

What is it?

The orientation or posture of an animal describes the way the animal’s body is rotated with respect to a fixed reference frame. Orientation can be a powerful tool for decoding behaviour. Many animals adopt task-specific postures; a good example is the stereotyped descent, horizontal swimming and ascent behaviour of a marine mammal dive cycle. For terrestrial animals, different postures may be associated with resting, foraging, vigilance, grooming, and submissive/dominant behaviour. The direction that an animal is pointing can also reveal attention, e.g., to social cues, predators, or human disturbance. But animals are not rigid bodies so tags can only tell us about the orientation of the part of the body where the tag is attached. For example, a tag attached to the back of a herbivore may be unable to record changes in head posture associated with foraging versus vigilance.

Although there are several ways mathematically to describe an animal’s orientation, the most common representation in biologging is the Euler angles: pitch, roll and heading (or yaw). These angles each describe the rotation of the body around a cardinal axis: for most animals these are the lateral, longitudinal and dorso-ventral axes, for pitch, roll and heading, respectively. This representation is easy to work with and is also biologically relevant as many animals use distinct muscles to change orientation in each of these angles, and use these turns in different behaviours. For example, a flying bird pitches up or down to change altitude, yaws to change direction, and rolls during evasive maneuvers.

How is it measured?

Pitch and roll are calculated from the triaxial accelerometer data by simple trigonometry (function a2pr()). Each of these angles describes how much the body is rotated away from a horizontal, dorsal-side-up posture. The pitch and roll are then used to ‘gimbal’ the magnetometer data, i.e., to rotate the triaxial data as if they came from a horizontal sensor (like those floating ships compasses). The heading, i.e., how much the longitudinal axis of the body is rotated away from north, is then calculated from the gimbaled magnetometer data (both steps are done using the function m2h()). To avoid having more than one way to describe each orientation, pitch is constrained to be within ±90°, and roll and heading are constrained to within ±180°. Although we usually talk about angles in degrees, the animaltags tools express these angles in radians. Remember to multiply the angles by 180/π to convert to degrees.

To compute pitch, roll and heading, the accelerometer and magnetometer data need to have the same sampling rate. Accelerometers are often sampled at a higher rate than magnetometers, and so acceleration data must be decimated to match the sampling rate of the magnetometer (e.g., using decdc()) before computing heading. It may also be necessary to low-pass filter the data before computing orientation. Accelerometers are sensitive to both orientation and specific acceleration, and the latter can cause errors in the orientation estimate. For example, a sharp forward acceleration of the animal will lead to an error in the pitch angle and, via gimballing, an error also in the heading. Specific acceleration tends to occur at the locomotion rate (i.e., the frequency of cyclic movements used to propel the animal) and higher, whereas posture changes tend to be slower. Applying a low-pass filter or smoother to the accelerometer data before computing orientation can therefore reduce errors due to specific acceleration (see Complementary filter tutorial). The accuracy of the pitch, roll and heading also depends on how well the accelerometer and magnetometer data are calibrated (see spherical_cal() tutorial and function).

What is it good for?

The pitch, roll, and heading angles are useful for behavioral sequencing and for detecting specific behaviors (e.g., foraging vs vigilance, diving vs searching, resting). The Euler angles are often easier to interpret than the raw accelerometer and magnetometer data, e.g., when plotted against time. For example, plots of the Euler angles synchronized to prey capture attempts can help to define search tactics (Izadi et al., 2021). Preferences for turns in one direction might indicate lateralization (Friedlaender et al., 2017). Orientation can be used also to determine the direction of travel or gaze. Combined with GPS position or visual sightings, the heading can be used to test for attraction to, or avoidance of, a playback at a known location (Nowacek et al., 2003).

As with angles in general, care is needed when using statistical methods to describe or test Euler angles. For example, a dog rolling on its back can have a roll angle that varies rapidly between +180° and -180° according to whether the dog is momentarily slightly more on its left or right side. Taking the mean of the Euler angles would give an apparent roll close to 0°. In this case, you could use a circular mean (Matlab tool circ_mean()) or you can equivalently take the mean of the accelerometer and magnetometer data before calculating the orientation.

The definition of the Euler angles with respect to a fixed frame can make them poorly-suited for describing dynamics in orientation, e.g., due to locomotion, especially in aquatic animals. For example, a dolphin can perform the same caudal propulsion movement (which involves a pitching rotation) when upright or rolled on its side. In representing these compound behaviors, it can be useful to define an overall, slowly-changing, body posture to which are added orientation dynamics (Martín López et al. 2016).

Technical description

Usage of tool

Pitch and roll estimation from triaxial accelerometer data. This is a non-iterative estimator with |pitch| constrained to <= 90 degrees. The pitch and roll estimates give the least-square-norm error between A (acceleration) and the A-vector that would be measured at the estimated pitch and roll. If A is in the animal frame, the resulting pitch and roll define the orientation of the animal with respect to its navigation frame. If A is in the tag frame, the pitch and roll will define the tag orientation with respect to its navigation frame.

It is important to note that the a2pr() function assumes a [north,east,up] navigation frame and a [forward,right,up] local frame. In these frames, a positive pitch angle is an anti-clockwise rotation around the y-axis. A positive roll angle is a clockwise rotation around the x-axis. A descending animal will have a negative pitch angle while an animal rolled with its right side up will have a positive roll angle.

[pitch,roll] = a2pr(A,fs,fc);

[pitch,roll] <- a2pr(A,fs,fc)

Inputs:

Outputs:

The m2h() function is used to compute the heading, field intensity, and the inclination angle by gimballing the magnetic field measurement matrix with the pitch and roll estimated from the accelerometer matrix. This requires both accelerometer and magnetometer data because the magnetometer data have to be ‘gimballed’ by the pitch and roll to make the heading measurement that would have been made by a horizontal tag. As with a2pr() function, m2h() assumes a [north,east,up] navigation frame and a [forward,right,up] local frame. North and east are magnetic, not true. In these frames a positive heading is a clockwise rotation around the z-axis.

 [heading,v,incl] = m2h(M,A,fs,fc);

 [heading,v,incl] <- m2h(M,A,fs,fc)

Inputs:

Outputs:

Notes:

Deep-Dive on Functionality

Lets compute the orientation angles, pitch roll and heading of a harbor seal from the calibrated accelerometer and magnetometer data in the animal frame. As we mentioned above, applying a low-pass filter or smoother to the accelerometer data before computing orientation may be needed before computing orientation to reduce errors due to the specific acceleration. This is because accelerometers are sensitive to both orientation and specific acceleration, and the latter can cause errors in the orientation estimate. Specific acceleration tends to occur at the locomotion rate (i.e., the frequency of cyclic movements used to propel the animal) and higher, whereas posture changes tend to be slower. If we low-pass filter the accelerometer data, we will need to apply the same filter to the magnetometer data before estimating heading.

Load the test dataset testset6.nc, which belongs to the data recorded from a tag glued to the back of a harbor seal [Note]This dataset has already been converted from a source file that was offloaded from the tag into a NetCDF file. In doing so, some metadata was gleaned from the file and added to the data. Other metadata was added by hand.. This dataset is built into the tagtools package, so you can access it using system.file.

pv_file_path = testset6.nc
pv = load_nc(pv_file_path)

pv_file_path <- system.file("extdata", "testset6.nc", package = 'tagtools', mustWork = TRUE)
xx <- load_nc(pv_file_path )

This dataset includes a series of dives and we want to infer their function by looking at theorientation, i.e., the pitch, roll and heading angles. Aa should contain acceleration data like what would have been recorded by a tag aligned with the animal’s axes, i.e., in the animal frame. Compute pitch and roll from Aa and heading from Aa and Ma, and plot them to check they make sense:

[pitch,roll] = a2pr(pv.Aa)
[heading,v,incl] = m2h(pv.Ma,pv.Aa)

[pitch,roll] <- a2pr(xx$Aa)
[heading,v,incl] <- m2h(xx$Ma,xx$Aa)

The pitch, roll and heading vectors are in radians (hence the *180/pi to covert to degrees) and have the same sampling rate as Aa and Ma.

Plot pitch, roll and heading. Zoom in to check if the animal is in a realistic orientation when it is at the surface, or during an ascent or descent.

fs = pv.A.sampling_rate;
plott(pv.P.data,fs ,pitch*180/pi,fs ,roll*180/pi,fs ,heading*180/pi,fs)
subplot(411)
ylabel('Depth')
axis ij
subplot(412)
ylabel('pitch')
subplot(413)
ylabel('roll')
subplot(414)
ylabel('head')

plott(X = list(`Depth m` = pv$P$data, `pitch (deg)` = pitch*180/pi, `roll (deg)` = roll*180/pi, `heading (deg)` = heading*180/pi) , fsx = sampling_rate)

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• MATLAB Output
• R Output

MATLAB Output

R Output

Coming soon …

We can see that the signal is a bit messy as pitch roll and heading orientation angles also contain high frequency information from the stroking signal. So, to clear these orientation signals we are going to smooth them. The code below will compute the smoothed pitch and roll angles. In order to select the cut-off frequency, fc, for the low pass filter to produce the smoothed pitch and roll angles. As mentioned in the complementary filter tutorial, a good starting choice for the filter cut-off frequency to separate low from mid and high frequency acceleration movements is 70% of the dominant stroking rate, but cut-off frequencies of 50 to 70% the dsf could be good options. If you have not done so, have a look at the dsf and complementary filter tutorials before continuing.

dsfa = dsf(beb.Aa) % 0.17 estimated stroking rate in Hz from the accelerometer data
fc = 0.70*dsfa %this is approximately 70% of the dsf (0.35 Hz)
Af  = comp_filt(A, fc);
Alow =  Af{1}; % low frequency A data

To verify that we have done this correct, we can plot the animal acceleration Aa, along with the low frequency accelerometer data, Alow and zoom in in the first dive.

plott(pv.P,fs,pv.Aa,fs, Alow,fs)
subplot(311)
ylabel('Depth m')
axis ij
subplot(312)
ylabel('Aa')
subplot(313)
ylabel('Alow')
xlim([0 0.08])

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• MATLAB Output
• R Output

MATLAB Output

R Output

Coming soon …

Lets estimate and plot the smoothed orientation angles obtained from the Alow signal along with the non-smoothed orientation angles.

[smoothpitch,smoothroll]=a2pr(Alow);
%check the difference between pitch and smoothpitch
figure; 
ax1 = subplot(3,1,1);
plot((1:length(P.data))/fs/3600,P.data)
axis ij
ylabel('Depth m')
ax2 = subplot(3,1,2);
plot((1:length(P.data))/fs/3600,pitch*180/pi)
hold on
ylabel('Pitch')
plot((1:length(P.data))/fs/3600,smoothpitch*180/pi,'k')
legend('pitch','smoothpitch')
ax3 = subplot(3,1,3);
plot((1:length(P.data))/fs/3600,roll*180/pi)
hold on
ylabel('Roll')
plot((1:length(P.data))/fs/3600,smoothroll*180/pi,'k')
legend('roll','smoothroll')
xlabel('Time hours')
linkaxes([ax1 ax2 ax3], 'x');

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• MATLAB Output
• R Output

MATLAB Output

R Output

Coming soon …

The tagtools use the convention that a negative pitch means nose down and a negative roll means right-side down. Zoom in to one of the dives at the start of the recording and verify that pitch is negative during the descent and positive in the ascent.

It can be easier to see different behaviours at the bottom of dives by ‘turning off’ the pitch and roll when the animal is not at the bottom:

smoothpitch_b=smoothpitch ;% make a copy of the pitch
smoothpitch_b(P.data<23)=NaN ;% blank out the pitch when the seal is shallower than 23 m
smoothroll_b=smoothroll ;% make a copy of the roll
smoothroll_b(P.data<23)=NaN ;% blank out the roll when the seal is shallower than 23 m

figure
plott(P,smoothpitch_b*180/pi,fs,smoothroll_b*180/pi,fs)
subplot(311);
ylabel('Depth m')
subplot(312);
ylabel('Smoothpitch')
subplot(313);
ylabel('Smoothroll')
linkaxes([ax1 ax2 ax3], 'x');

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• MATLAB Output
• R Output

MATLAB Output

R Output

Coming soon …

Now check out the surface orientation of the seal:

smoothpitch_s=smoothpitch ;% make a copy of the pitch
smoothpitch_s(P.data>5)=NaN ;% blank out the pitch when the seal is shallower than 23 m
smoothroll_s=smoothroll ;% make a copy of the roll
smoothroll_s(P.data>5)=NaN ;% blank out the roll when the seal is shallower than 23 m


figure; 
plott(P,smoothpitch_s*180/pi,fs,smoothroll_s*180/pi,fs)
subplot(311);
ylabel('Depth m')
subplot(312);
ylabel('Smoothpitch')
subplot(313);
ylabel('Smoothroll')
linkaxes([ax1 ax2 ax3], 'x');

Expand to show figure …

• MATLAB Output
• R Output

MATLAB Output

R Output

Coming soon …

Orientations can be hard to visualize, and an animation is sometimes helpful. To make a full animation of orientation, we are going to use the plot_3d_model() tool that will show a whale (reflecting the taxonomic bias of its authors!) that is animated by pitch, roll and heading data. First create the plot and get a structure that will allow you to animate it:

figure
F = plot_3d_model;

Now select a small piece of data so that the animation doesn’t take too long. Here we are using the unsmoothed pitch and roll as these ones will also show the stroking motions. The following will produce a 210 second clip of pitch, roll and heading data from one of the early dives, and animate the whale with this segment of data:

k=1018*fs:1228*fs;% pick out section from second 1018to 1228
prh=[pitch(k),roll(k),heading(k)];
rot_3d_model(F,prh)

The animation goes much faster than real time. Try to follow the animation on the dive profile figure to see where in the dive the seal is. Now try animating one of the dives in the middle of the recording, e.g., from second 14180 to 14610.

k=14180 *fs:14610*fs;% pick out section from second 1018to 1228
prh=[pitch(k),roll(k),heading(k)];
rot_3d_model(F,prh)

Caveats

There are two peculiar features of Euler angles. The first is that the sequence of rotations matters: to interpret the orientation of an animal, think of a hypothetical horizontal and north-pointing animal. Then apply the heading, pitch and roll angles, in that order, to rotate the animal to its actual orientation. Changing the order will give a different orientation. The second feature is called ‘gimbal lock’ and refers to an ambiguity between roll and heading when the pitch angle is ±90°. Gimbal lock can arise when animals dive or fly steeply, and is unavoidable in upright bipedal animals (when you are lying down you can roll over without changing your heading; can you do that when standing up?). One consequence of gimbal lock is that small errors in acceleration get amplified into large errors in roll when the pitch angle is nearly vertical – be cautious in interpreting the roll angle when the absolute pitch is greater than about 70°.

References

If you would like to know more about seal behavior you can refer to the following papers:

Vance, H.M., Hooker, S.K., Mikkelsen, L. et al. Drivers and constraints on offshore foraging in harbour seals. Sci Rep 11, 6514 (2021). https://doi.org/10.1038/s41598-021-85376-2

Mikkelsen, L. et al. Long-term sound and movement recording tags to study natural behavior and reaction to ship noise of seals. Ecol. Evol. 9(5), 2588–2601 (2019). https://doi.org/10.1002/ece3.4923