Search theory for search and rescue planning

LateralRange: definite range, M-Beta and inverse cube (Koopman) lateral range curves with sweep width W. SweepWidth: area under a sampled lateral range curve. SearchPod: POD from coverage for random search, definite range and inverse cube parallel sweeps. ParallelSweepPod: numerical parallel-sweep POD for any model, with optional normal navigation error. SearchSuccess: POS, Bayesian POC updating, cumulative POD and POS. DatumProbabilityMap: point, line and area datum cell probabilities. OptimalCircularSearch: Koopman's optimal effort for a circular normal datum. OptimalEffortAllocation: optimal effort over cells (Stone 1975). Identical to the Python arm morie.fn.searchth.

Usage

LateralRange(x, W, model = "inverse_cube", m = 1)

SweepWidth(x, p)

SearchPod(coverage, model = "random")

ParallelSweepPod(
  W,
  S,
  model = "inverse_cube",
  m = 1,
  nav_sd = 0,
  n_points = 2001,
  n_tracks = 60
)

SearchSuccess(poc, pod)

DatumProbabilityMap(
  x_edges,
  y_edges,
  datum = "point",
  center = c(0, 0),
  sigma = 1,
  end = NULL,
  nodes = 64
)

OptimalCircularSearch(sigma, W, effort)

OptimalEffortAllocation(poc, area, W, effort, tol = 1e-14)

Arguments

x

Lateral ranges or abscissae.

W

Sweep width.

model

Detection model.

m

M-Beta height.

p

Lateral range values.

coverage

Coverage values.

S

Track spacing.

nav_sd

Navigation error standard deviation.

n_points, n_tracks

Quadrature controls.

poc, pod

Containment and detection probabilities (pod a vector, or a matrix with one row per search).

x_edges, y_edges

Grid cell edges.

datum

"point", "line" or "area".

center, end

Datum coordinates.

sigma

Circular normal standard deviation.

nodes

Gauss-Legendre nodes along a line datum.

effort

Total effort (track length).

area

Cell areas.

tol

Bisection tolerance.

Value

Numeric or list.

References

Koopman, B. O. (1946). Search and Screening. OEG Report 56, Office of the Chief of Naval Operations.

Frost, J. R. (1996). The Theory of Search: A Simplified Explanation. Soza and Company and U.S. Coast Guard Office of Search and Rescue.

Stone, L. D. (1975). Theory of Optimal Search. Academic Press.

Examples

LateralRange(c(0.5, 1, 2), 1)
#> [1] 0.27262265 0.07649353 0.01969778
SearchPod(1, model = "inverse_cube")
#> [1] 0.7899086
OptimalCircularSearch(1, 1, pi / 4)$pos
#> [1] 0.09020401