Auto-Calibrate Raw Acceleration to the Unit Gravity Sphere

Estimates per-axis gain and offset corrections by the van Hees et al. (2014) method: during non-movement windows the acceleration vector should lie on the 1 g sphere, so gain/offset are fit by iteratively projecting non-movement window means onto the closest point of the unit sphere. Apply as (raw - offset) * scale.

Usage

auto.calibrate(
  xyz,
  fs,
  sphere_crit = 0.3,
  sd_crit = 0.013,
  max_iter = 1000,
  tol = 1e-10
)

Arguments

xyz

A data frame or matrix of raw acceleration in g (columns x, y, z).

fs

Sample rate in Hz.

sphere_crit

Minimum coverage (g) each axis must span on both sides of zero for a stable fit (default 0.3).

sd_crit

Per-axis SD (g) over consecutive (non-overlapping) 10-second windows below which a window counts as non-movement (default 0.013).

max_iter

Maximum refinement iterations (default 1000).

tol

Convergence tolerance on the calibration error (default 1e-10).

Value

A list with scale and offset (length-3), the calibration error before and after (cal_error_start, cal_error_end, mean absolute deviation from 1 g), npoints, a calibrated flag, and a reason string describing the outcome. When there is too little non-movement data the identity correction is returned with calibrated = FALSE.

References

van Hees VT, Fang Z, Langford J, Assah F, Mohammad A, da Silva ICM, Trenell MI, White T, Wareham NJ, Brage S (2014). “Autocalibration of accelerometer data for free-living physical activity assessment using local gravity and temperature: an evaluation on four continents.” Journal of Applied Physiology, 117(7), 738–744. doi:10.1152/japplphysiol.00421.2014 .

Examples

# Recover a known per-axis gain and offset from non-movement windows
set.seed(1)
u <- matrix(rnorm(40 * 3), 40, 3); u <- u / sqrt(rowSums(u^2))   # sphere directions
raw <- do.call(rbind, lapply(seq_len(40), function(i)
  matrix(rep(u[i, ] / c(1.03, 0.97, 1.01) + c(0.04, -0.03, 0.02), each = 300),
         300, 3) + rnorm(900, 0, 0.004)))
auto.calibrate(data.frame(x = raw[, 1], y = raw[, 2], z = raw[, 3]), fs = 30)$scale
#> [1] 1.0301368 0.9701036 1.0099053