For the full theoretical description, refer to complementary filter – technical explanation.
X:A sensor vector or matrix (i.e., with a signal in each column) or sensor list.
sampling_rate:The sampling rate of the sensor data in Hz (samples per second).
fc:(optional). Specifies the cut-off frequency or frequencies of the complementary filters. Frequencies are in Hz. If one frequency is given, X will be split into a low- and a high-frequency component. If fc contains more than one value, X will be split into multiple complementary bands.
Xf:The dominant stroke frequency (i.e., the peak frequency in the sum of the acceleration power spectra) in Hz. There are n+1 cells where n is the length of fc. Cells are ordered in Xf from lowest to highest frequency. Each cell contains a vector or matrix of the same size as X, and at the same sampling rate as X.
Locomotion in many animals involves the oscillatory movement of limbs, fins or wings. These oscillations tend to occur at the dominant stroke frequency (dsf) and are overlaid on the constantly changing postural orientation, which tend to occur at a lower rate, as the animal manoeuvres. To separate these two signals that occur at a different rate, we can use a complementary filter using the
comp_filt() function. For the full theoretical description, refer to complemetary filter – technical explanation.
In this vignette, you will learn how to use complementary filters, using the
comp_filt() function, to separate intervals of movements into distinct frequency bands, i.e., animal orientation (low frequency), gait (mid frequency or dsf) and strikes/flinches (high frequency), in order to gain insight about the locomotion and biomechanical strategies of different aerial, terrestrial and marine animals. For the full technical description, refer to complementary filter – technical explanation.
To verify that you have run
correctly, i.e., that you have set the filter cut off frequencies correctly, to seperate orientation from gait from strikes you will need to plot each signal separately and check that they look as they should. For the full verification, refer to complementary filter – technical explanation.
As with any filter, if the cut-off frequency to separate orientation from gait locomotion is too low, the magnitude of the gait locomotion will be overstimated and the animal orientation will be mistakenly identified as strokes. On the other hand is this cut-off frequency is too high, the magnitude of the gait locomotion will be understimated and the stroking will be visible in the animal orientation, i.e., low-frequency signal. For the full verification, refer to complementary filter – technical explanation.
Load and Visualize the Test Data Set
Load the test dataset
Brydes_test, which belongs to the data recorded from a suction cup tag attached to the back of a Bryde’s whale published in Izadi et al. (2022) [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
plott() to inspect it:
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This dataset contains few consecutive surface lunges. We want to describe the biomechanical locomotion of this animal, and so we will separate the animal orientation (low frequency) from the stride, flap or fluke motion (mid frequency) from the rapid muscle movements and unsteady flow (high-frequency).
For tags not glued, attached with suction cups, it could happen that the tag is not properly attached (2 out of 4 suction cups attached) or that 2 out of 4 suction cups get detached earlier than the other 2 and so the tag vibrates. Stroking periods of the animal deployment should resemble a smooth sine wave in the acceleration data. However, if this are spiky such as in the figure below this may be an indication that the tag is vibrating, and we should try to remove that noise. If you need to do this on your data, please check the Remove high frequency noise due to tag vibration tutorial before you continue.
To separate slow changes in orientation from stride, flap, or fluke motion dynamics in locomotion, and from rapid muscle movements we need to choose a filter cut-off frequency below the stride, flap, or fluke stroke frequency. We can estimate the dominant stroke frequency using dsf(). Go to the dominant stroke frequency tutorial for a greater detail on how to estimate it and use the dsf() function.
beb.Aa to get the mean stroking rate:
dsfa is 0.35 Hz (from Izadi et al., 2022).
A good starting choice for the filter cut-off frequency of the complementary filter to separate low and mid frequency acceleration movements is 70% of the dominant stroking rate, but cut-off frequencies of 50 to 70% the dsf could be good options. Call this value
fc1. Depending on your reserach question you should use a different cut-off frequency. In fact, Izadi et al. (2022) used a cut-off frequency of 0.17 which is approximately 50% of the dsf during lunges.
What differences do you expect to obtain in the output of comp_filt compared to Izadi’s?
A cut-off frequency filter of 70% the dsf would let pass more high frequencies than a 50% one. This means that for the cut-off frequency filter of 70%, the magnitude of the gait locomotion will be smaller and the stroking will be visible in the animal orientation, i.e., low-frequency signal. To verify that you have set this cut-off frequency correctly, you will need to plot each signal separately and check that they look as they should. Refer to the verification section for a greater detail.
To further separate the mid from the high frequency accelerometer data we need to set a second cut-off frequency filter,
fc2. To get all the information regarding stroking in the mid frequency acceleration signal, fc2 should be at least twice the stroking rate of interest. In this case we will set
fc2 to 0.8Hz being approximately twice the stroking rate during surface lunges.
Run a complementary filter on
Aa to separate the slow, mid and fast time-scales. Recall that
Aa is stored under
The complementary filter returns a structure containing three data matrices: the low-pass filtered data, mid-pass filtered data and the high-pass filtered data. Each of these is a three-column matrix because the filter is run on each column of the input data. So, it is like you now have three accelerometers in the tag: one is only sensitive to low frequencies, another is only sensitive to mid frequencies, and the other is only sensitive to high frequencies. If you would like to get each matrix out of the cell array, do:
The sampling rate of these is the same as for the original data. For simplicity, make a variable
sampling_rate equal to the sampling rate and use plott() to plot the three filtered accelerations along with the dive profile:
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The low and mid versions of acceleration are sometimes called ‘static’ and ‘dynamic’ acceleration. If the filtering worked, you should see that
Alow has large, relatively slow changes in acceleration which are mostly to do with orientation. These are missing in
Amid has the mid frequency specific acceleration, having to do with propulsion (stride, fluke or flap), and
Ahigh has the high frequency acceleration which has to do with rapid muscle movements such as strikes and flinches, and unsteady flow.
You could estimate animal orientation, pitch and roll of the animal from this low frequency acceleration. If you want to also estimate the heading of the animal you need to get the low frequency magnetometer data in the same way as you did for the accelerometer. Go through the animal orientation technical explanation for greater detail on how to estimate pitch, roll and heading and use the a2pr() and m2h() functions.
Izadi, S., Aguilar de Soto, N., Constantine, R., & Johnson, M. (2022). Feeding tactics of resident Bryde’s whales in New Zealand. Marine Mammal Science, 1–14. https://doi.org/10.1111/mms.12918