inst/doc/Chapter_AnimalTracking.R

In gragusa/MARSS: Multivariate Autoregressive State-Space Modeling

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### code chunk number 20: Cs5_code
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###############################################################
#    GCDF FUNCTION
#    This function converts units of degrees lat/lon to miles, 
#    nautical miles, or kilometers
###############################################################
GCDF <- function(lon1, lon2, lat1, lat2, degrees=TRUE, units="miles") {
   # This is the function for the Great Circle Distance Formula 
   # using decimal degrees or radians
   # Calculations at: http://www.nhc.noaa.gov/gccalc.shtml
   # This first component is only dependent on degrees or radians
   temp = ifelse(degrees==FALSE, acos(sin(lat1) *  
   sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1)), 
   acos(sin(lat1/57.2958) * sin(lat2/57.2958) + cos(lat1/57.2958) 
   * cos(lat2/57.2958) *  cos(lon2/57.2958 -lon1/57.2958)))
   r=3963.0 # (statute miles) , default
   if("units"=="nm") r=3437.74677 # (nautical miles)
   if("units"=="km") r=6378.7 # (kilometers)
   return (r * temp)
}

library(maps)    # must be installed from CRAN

# our noisy data (with no missing values)
turtles = levels(loggerheadNoisy$turtle)
levels(loggerheadNoisy$turtle)

##############SPECIFY THE TURTLE NAME HERE
turtlename="BigMama"

dat = loggerheadNoisy[which(loggerheadNoisy$turtle==turtlename),5:6]
dat = t(dat)

# Set up the MSSM model
# We are going to make a big approximation:
# We are going to pretend that 1 deg longitude 
# change is equal to about the same distance (miles)
# over the range of latitudes that the turtles are moving
# That's not true.  There is about a 10% difference across
# their range of latitude movement.
Q.model="diagonal and unequal"
R.model="diagonal and unequal"
U.model="unequal"
Z.model="identity" 

# Fit a random walk model for lon/lat to the lon/lat data
kem = MARSS(dat, model=list(Z = Z.model, 
   Q = Q.model, R = R.model, U = U.model))
pred.lon = kem$states[1,]
pred.lat = kem$states[2,]

##########################################
# Plot the results
##########################################
op = par(mai = c(0,0,0,0))
map('state', region = c('florida', 'georgia', 
   'south carolina', 'north carolina', 'virginia', 
   'delaware','new jersey','maryland'),xlim=c(-85,-65))
points(loggerheadNoisy$lon[which(loggerheadNoisy$turtle==turtlename)], 
   loggerheadNoisy$lat[which(loggerheadNoisy$turtle==turtlename)], 
   col="blue",pch=21, cex=0.7)
lines(pred.lon, pred.lat,col="red", lwd=2)

# add the good location data
goodturtles = loggerhead
gooddat = goodturtles[which(goodturtles$turtle==turtlename),5:6]
points(gooddat[,1], gooddat[,2],col="black", lwd=2, pch=3, cex=1.1)
legend("bottomright",c("bad locations", "estimated true location", "good location data"),pch=c(1,-1,3),lty=c(-1,1,-1),col=c("blue","red","black"),bty=F)

# add the proposed fishery areas
lines(c(-77,-78,-78,-77,-77),c(33.5,33.5,32.5,32.5,33.5),
   col="red",lwd=2)
lines(c(-75,-76,-76,-75,-75),c(38,38,37,37,38),
   col="red",lwd=2)

###########################################
# Calculate the average miles traveled each day using
# the function GCDF defined above
# You must select and run the GCDF code first
###########################################
distance = array(NA, dim=c(dim(dat)[2]-1,1))
for(i in 2:dim(dat)[2])
   distance[i-1]=GCDF(pred.lon[i-1],pred.lon[i],
   pred.lat[i-1],pred.lat[i])

par(op) #reset plotting pars back to normal
par(mfrow=c(1,2))  #make a 2 panel graph
hist(distance) #make a histogram of distance traveled per day
print(paste("KalmanEM estimate of ave. mile per day for ",
  turtlename," = ", mean(distance) ))

# Compare to the distance traveled per day if you used the raw data
distance = array(NA, dim=c(dim(dat)[2]-1,1))
for(i in 2:dim(dat)[2])
   distance[i-1]=GCDF(dat[1,i-1],dat[1,i],dat[2,i-1],dat[2,i])
hist(distance) #make a histogram of distance traveled per day
mean(distance) 
print(paste("Raw estimate of ave. mile per day for ",
  turtlename," = ", mean(distance) ))