stopdetection (version 0.1.2)

radiusOfGyrationDT: Radius of Gyration

Description

Calculates the time-weighted radius of Gyration provided a data.table containing latitude, longitude and a timestamp. This is the root-mean-square time-weighted average of all locations. Weighting by time is provided to adjust for unequal frequency of data collection.

Usage

radiusOfGyrationDT(lat_col, lon_col, timestamp, dist_measure = "geodesic")

Value

Time-weighted radius of gyration

Arguments

lat_col

Time-ordered vector of latitudes

lon_col

Time-ordered vector of longitudes

timestamp

Timestamps associated with the latitude/longitude pairs

dist_measure

Passed through to geodist::geodist_vec, One of "haversine" "vincenty", "geodesic", or "cheap" specifying desired method of geodesic distance calculation.

Details

Time-weighted RoG is defined as $$ \sqrt{\frac{\sum_i{w_j \times dist([\overline{lon}, \overline{lat}], [lon_j, lat_j]})}{\sum_i{w_j}}}$$ Where $$\overline{lon} = \frac{ \sum_j w_j lon_j}{\sum_j w_j} \quad \textrm{and} \quad \overline{lat} = \frac{ \sum_j w_j lat_j}{\sum_j w_j}$$ And the weighting element \(w_j\) represents half the time interval during which a location was recorded $$w_j = \frac{t_{j+1} - t_{j - 1}}{2}$$

Examples

# Inside a data.table
dt <- data.table::data.table(
  lat = c(1, 1, 1, 1, 1),
  lon = c(1, 1.5, 4, 1.5, 2),
  timestamp = c(100, 200, 300, 600, 900)
)
dt[, radiusOfGyrationDT(lat, lon, timestamp)]
# As vectors
radiusOfGyrationDT(
  c(1, 1, 1, 1, 1),
  c(1, 1.5, 4, 1.5, 2),
  c(100, 200, 300, 600, 900)
  )