Creating a utilization distribution of telemetry data using the circular normal model [closed]

Question

I am trying to replicate a procedure performed in Ramsey et al. 2022 to assess the efficiency of radio tracked animals in locating conspecifics for removal. This procedure uses a utilization distribution for each animal calculated using the circular normal model for the simplicity of the univariate distribution that this model generates. I'm familiar with MCPs and KDEs, but I have had no luck so far in figuring out how to create utilization distributions with the circular normal model. I think I may need to first convert my coordinates to polar coordinates based on this quote from Van Winkle, 1975 "...the utilization distribution is a bivariate frequency distribution. It can, however, be reduced to a univariate distribution by transforming from cartesian coordinates (X,Y) to polar coordinates (θ,r), and summing over θ from 0 to 2π for suitably small intervals of the radial distance r.", but I am a little lost on what to do after transforming from cartesian to polar coordinates. Does anyone know how I might go about creating this utilization distribution?

Example code:

#Step 1: creating a sample data frame
x<-sample(seq(from = 410293.3, to = 450426.6, by = 1), size = 10, replace = TRUE)
y<-sample(seq(from = 2865107, to = 2892925, by = 1), size = 10, replace = TRUE)

#step 2: convert cartesian to polar coordinates

#function to calculate r
cart2pol.r <- function(x, y)
{
  r <- sqrt(x^2 + y^2)
  c(r)
}

#function to calculate theta
cart2pol.t <- function(x, y)
{
  t <- atan(y/x)
  c(t)
}

#apply functions and assemble into dataframe of polar coordinates
coords.polar.r<-cart2pol.r(x=x,y=y)
coords.polar.t<-cart2pol.t(x=x,y=y)

coords.polar<-data.frame(coords.polar.r, coords.polar.t)


#Step 3: create utilization distribution from the polar coordinates using the circular normal method. This is where I'm lost