Mean Amplitude Deviation (MAD) acceleration metric

MAD is the mean absolute deviation of the tri-axial acceleration vector magnitude about its (per-epoch) mean (Vaha-Ypya et al. 2015): for each epoch, \({\rm MAD} = \frac{1}{n}\sum_i |r_i - \bar r|\), where \(r_i = \sqrt{x_i^2 + y_i^2 + z_i^2}\) is the sample vector magnitude and \(\bar r\) its epoch mean. It is a gravity-robust movement-intensity metric complementary to computeENMO: MAD captures the amount of variation in the magnitude within an epoch (so it is insensitive to a static orientation offset), whereas ENMO captures its elevation above 1 g. When an epoch length is given, per-epoch MAD is returned; otherwise a single whole-signal MAD.

Usage

computeMAD(accel, sampling_rate = NULL, epoch_sec = NULL, unit = c("g", "mg"))

Arguments

accel: An n x 3 matrix (or data frame) of acceleration in g units (columns x, y, z).
sampling_rate: Sampling rate in Hz (required if epoch_sec is set).
epoch_sec: Epoch length in seconds for aggregation; NULL returns a single MAD over the whole signal.
unit: "g" (default) or "mg" (milli-g).

Value

A numeric vector of MAD values (one per epoch, or a single value).

References

Vaha-Ypya H, et al. (2015). Clin Physiol Funct Imaging 35(1):64-70.

Examples

set.seed(1)
acc <- matrix(rnorm(300, c(0, 0, 1), 0.1), ncol = 3, byrow = TRUE)
computeMAD(acc)                       # whole-signal MAD (g)
#> [1] 0.07289114
computeMAD(acc, sampling_rate = 100, epoch_sec = 1)  # per-epoch MAD
#> [1] 0.07289114