range2CEP {shotGroups}

Estimate circular error probable (CEP) based on range statistics

Description

Estimate the circular error probable (CEP) based on range statistics such as extreme spread, figure of merit, or the bounding box diagonal. This function assumes a circular bivariate normal shot distribution with 0 mean.

Usage

range2CEP(x, stat="ES", n=5, nGroups=1, CEPlevel=0.5, CIlevel=0.95,
            collapse=TRUE, dstTarget, conversion)

Arguments

x

a numerical vector with values for extreme spread (ES), figure of merit (FoM), or the diagonal of the bounding box (D).

stat

a character vector with elements "ES" (extreme spread), "FoM" (figure of merit), or "D" (bounding box diagonal) indicating which range statistic is given in x. Elements correspond to those in x in the sense that the second element of stat indicates the statistic for the second element of x. If all elements of x are the same kind of statistic, stat only needs to indicate it once.

n

integer between 2 and 100. Number of shots in each group.

nGroups

integer between 1 and 10. Number of groups when x is the average of individually-measured range statistics from several groups.

CEPlevel

a numerical vector with the coverage values for the CEP.

CIlevel

confidence level (coverage probability) for the CEP confidence interval. If one of 0.5, 0.9, 0.95, 0.99, the CI is based on the corresponding quantiles of the Monte Carlo distribution of the range statistic for given n and nGroups. If not, CI can only be calculated for extreme spread using a Patnaik chi^2 approximation to the conditional distribution as suggested by Taylor and Grubbs (1975).

collapse

logical: should the list with CIs be simplified if possible?

dstTarget

a numerical value giving the distance to the target - used in MOA calculation. See getMOA.

conversion

how to convert the measurement unit for distance to target to that of the (x,y)-coordinates in MOA calculation. Example 'm2cm'. See getMOA.

Details

Based on the lookup table DFdistr with results form a Monte Carlo simulation. The Rayleigh sigma parameter is estimated using range2sigma, and then converted to CEP with qRayleigh.

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("range").

Value

A list with the calculated CEP values in one component, and the corresponding CIs in the other component.

CEP

The calculated CEP values in the original measurement unit as well as in angular size measures.

CEPCI

The calculated CEP CIs in the original measurement unit as well as in angular size measures.

References

Taylor, M. S., & Grubbs, F. E. (1975). Approximate Probability Distributions for the Extreme Spread (BRL-MR-2438). Aberdeen Proving Ground, MD: U.S. Ballistic Research Laboratory.

See Also

DFdistr, range2sigma qRayleigh getCEP

Examples

es  <- getMaxPairDist(DFscar17)$d
fom <- getBoundingBox(DFscar17)$FoM
d   <- getBoundingBox(DFscar17)$diag
range2CEP(c(es, fom, d), stat=c("ES", "FoM", "D"),
          n=nrow(DFscar17), nGroups=1, CEPlevel=0.5, CIlevel=0.9)

# compare with Rayleigh CEP estimate from using
# (x,y)-coordinates of all shots
getCEP(DFscar17, CEPlevel=0.5, type="Rayleigh")