# Technical Explanation – Minimum Specific Acceleration (MSA)

#### Theoretical description

What is it?

The Minimum Specific Acceleration (MSA) is an activity measure proposed in Simon et al. (2012). Specific acceleration is any acceleration generated by muscle contractions or imposed by external forces acting on the animal such as drag and lift. The term ‘specific’ is used to distinguish these accelerations from the acceleration due to gravity. These two terms are also known as dynamic and static acceleration, respectively. Both the specific and gravity acceleration are measured by animal-attached accelerometers and cannot be readily separated in the acceleration signals.

In ODBA, VeDBA and related activity measures, the specific acceleration is approximately separated from the gravity acceleration by filtering. MSA is another way to estimate the magnitude of the specific acceleration that has the advantage of not requiring a filter. However, compared to OBDA-type measures, it has the disadvantage of giving an underbound on the actual specific acceleration magnitude, i.e., the MSA is less than or equal to the true specific acceleration and so is a biased estimate.

How is it measured?

MSA is computed directly from the triaxial accelerometer data. The accelerometer data must be corrected for the sensitivity and offset of the sensor so that the signal for each axis is in units of m/s2. This can be done using predetermined calibration constants, or by fitting the observed triaxial measurements to a sphere with radius 9.81 m/s2. The MSA is sensitive to the accuracy of the calibration constants: errors in the calibration will give similar-sized errors in the MSA. However, MSA is completely insensitive to the orientation of the tag on the animal because it uses only the vector magnitude of the three accelerometer axes.

If At is the accelerometer vector at time t, calibrated to m/s2, the MSA at time t is computed by:

MSAt = | ||At||-9.81 |

where ||At|| is the vector magnitude of At, i.e., sqrt(At,x2+At,y2+At,z2). The outside single | means the absolute value. To understand this formula, imagine first that there is no specific acceleration. In this case, if the accelerometer is well-calibrated, ||At|| should be 9.81, i.e., the strength of earth’s gravity, and MSA will be zero. If there is some specific acceleration, ||At|| will be bigger, or possibly smaller than 9.81 (it depends on the direction of the specific acceleration). In either case, the MSA will be positive. As shown in Simon et al. (2012), the MSA is always less than or equal to the vector magnitude of the specific acceleration. If the orientation of the animal is largely uncorrelated with the specific acceleration, MSA will likely be a close estimate of the specific acceleration magnitude.

What is it good for?

MSA is useful as a general activity measure, e.g., for finding bouts of higher energy activity. It can also be used to test whether a particular behaviour involves specific acceleration or just orientation changes. MSA is particularly useful when the frequency range of specific acceleration and orientation changes can overlap, e.g., in foraging where there is both locomotion and rapid maneuvers. In this case, the spectral separation assumption in the ODBA methods breaks down resulting in biased measurements of activity intensity.

#### Technical description

Usage of tool

In this vignette you will learn to use msa() to gain insight about how to estimate the activity meassure called minimum specific acceleration (MSA).

MATLAB
```m = msa(A,ref)
```
R
```m <- msa(A,ref)
```
###### Inputs:
• `A`: An `nx3` acceleration matrix with columns `[ax ay az]`, or a tag sensor data list containing acceleration data. Acceleration can be in any consistent unit, e.g., g or m/s^2. `A` can be in any frame as the MSA is rotation independent.
• `ref`: The gravitational field strength in the same units as `A`. This is not needed if `A` is a sensor structure. If `A` is a matrix, the default value is 9.81 which assumes that `A` is in m/s^2. Use `ref = 1` if the unit of `A` is g.
###### Output:
• `m`: A column vector of MSA with the same number of rows as `A`, or a tag sensor data list (output matches input). `m` has the same units as `A`.

#### Caveats

As mentioned above, compared to OBDA-type measures, it has the disadvantage of giving an underbound on the actual specific acceleration magnitude, i.e., the MSA is less than or equal to the true specific acceleration and so is a biased estimate.

Simon M, Johnson M, and Madsen PT. (2012). Keeping momentum with a mouthful of water: behavior and kinematics of humpback whale lunge feeding. The Journal of Experimental Biology, 215(Pt 21), 3786–3798. https://doi.org/10.1242/jeb.071092