R/simutil-crw.r

In jsta/glatos: A package for the Great Lakes Acoustic Telemetry Observation System

#' Simulate a correlated random walk
#' 
#' Simulate a random walk as series of equal-length steps with turning angles 
#'   drawn from a normal distribution.
#'
#' @param theta A 2-element numeric vector with turn angle parameters 
#'   (theta[1] = mean; theta[2] = sd) from normal distribution.
#'   
#' @param stepLen A numeric scalar with total distance moved in each step.
#' 
#' @param initPos A 2-element numeric vector with nital position (initPos[1]=x, 
#'   initPos[2]=y).
#'   
#' @param initHeading A numeric scalar with initial heading in degrees.
#' 
#' @param nsteps A numeric scalar with number of steps to simulate.
#'
#' @details
#' First, nsteps turn angles are drawn from a normal distribution. Second, the 
#' cumulative sum of the vector of turn angles defines the heading within each 
#' step. The x and y component vectors in each are then calculated and summed 
#' to obtain the simualted path.
#' 
#' @return A two-column data frame containing:
#' \item{x}{x coordinates}
#' \item{y}{y coordinates}
#'
#' @author C. Holbrook (cholbrook@usgs.gov) 
#'
#' @note Adapted from code provided by Tom Binder.
#'
#' @examples
#' foo <- crw(theta=c(0,5), stepLen=10, initPos=c(0,0), initHeading=0, 
#'   nsteps=10)
#' plot(foo,type="o",pch=20,asp=c(1,1))
#'
#' @export
crw <- function(theta=c(0,5), stepLen=10, initPos=c(0,0), 
  initHeading=0,nsteps=10000){
      #generate turn angles
      heading <- rnorm(nsteps, mean=theta[1],sd=theta[2])
      heading <- initHeading + cumsum(heading)
      heading <- heading %% 360
      heading_rad <- heading * pi/180 #convert to radians
        
      #create steps
      xlen <- sin(heading_rad)*stepLen #x-component vector
      ylen <- cos(heading_rad)*stepLen #y-component vector
      path <- data.frame(
           x = as.numeric(initPos)[1] + cumsum(xlen),
           y = as.numeric(initPos)[2] + cumsum(ylen))
            
  return(path)
} #end crw def