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# Librairies nécessaire : plotrix
source(paste(dirname(sys.frame(1)$ofile),"/intersectionCercles.R",sep=""))
library("plotrix")
##############################
# Retourne la position estimée pour les différentes distance
# gwX = une matrice des coordonnées en X de chaque gateway (attention à l'odre avec gwY) exemple :
# gwX1,gwX2,gwX3
# gwY = une matrice des coordonnées en Y de chaque gateway (attention à l'odre avec gwX)
# distances = une matrice, exemple pour trois gateway avec 4 points à trouvées :
#
# d1gw1,d2gw1,d3gw1,d4gw1
# d1gw2,d2gw2,d3gw2,d4gw2
# d1gw3,d2gw3,d3gw3,d4gw3
#
# stepByStep = si a TRUE alors affiche la multilatération pour chaque points
# precisionPlot = nombre d'unité en X et en Y lors de l'affichage de la multilatération pour chaque points
##############################
multilateration=function(gwX,gwY,distances,stepByStep=FALSE,precisionPlot=80){
# Check parameters
if(!is.vector(gwX)){
stop("gwX is not a vector")
}
else if(!is.vector(gwY)){
stop("gwY is not a vector")
}
else if(!is.matrix(distances)){
stop("distances is not a matrix")
}
else if(length(gwX)!=length(gwY)){
stop("gwX and gwY haven't the same length")
}
else if(NROW(distances)!= length(gwX)){
stop("Number of rows of distances have not the same length of the gwX and gwY")
}
# Init convenience variables
nbGw=length(gwX);
nbDistances=NCOL(distances)
# Get the middle point of a segment
getMiddleOfSegment=function(x1,y1,x2,y2){
x=(x1+x2)/2;
y=(y1+y2)/2;
return(c(x,y));
}
# Get line equation from two of his points y=ax+b
getLineEquation=function(x1,y1,x2,y2){
eq=NULL;
if(x1!=x2){
a=(y1-y2)/(x1-x2);
b=y1-a*x1;
eq=c(a,b);
}
return(eq);
}
# Get line equation of 2 circles intersections points
getIntersectionLineEquation=function(circlesIntersections){
if(NROW(circlesIntersections)>1){
lineEquation=getLineEquation(
circlesIntersections[1,1],circlesIntersections[1,2],
circlesIntersections[2,1],circlesIntersections[2,2]);
if(is.null(lineEquation)){
return(circlesIntersections[1,1]);
}
return(lineEquation);
}
return(NULL);
}
# Build solution for each distances
sol=NULL;
for(i in 1:nbDistances){
linearLines=NULL;
xLines=NULL;
currentSol=NULL;
circlesIntersections=NULL;
# Build lines equation for linearLines and xLines
for(j in 1:(nbGw-1)){
mainGw=c(gwX[j],gwY[j]);
for(k in (j+1):nbGw){
slaveGw=c(gwX[k],gwY[k])
currentCirclesIntersections=getIntersection(mainGw[1],mainGw[2],distances[j,i],slaveGw[1],slaveGw[2],distances[k,i]);
circlesIntersections=rbind(circlesIntersections,currentCirclesIntersections);
lineEquation=getIntersectionLineEquation(currentCirclesIntersections)
if(length(lineEquation)==1){
xLines=rbind(xLines,lineEquation)
}
else{
linearLines=rbind(linearLines,lineEquation)
}
}
}
# Build lines intersections
intersections=NULL;
if(NROW(linearLines)>0||length(xLines)>0){
# Get intersections with xLines
sapply(xLines,function(x){
if(NROW(linearLines)>0){
apply(linearLines,1,function(eq){
intersections<<-rbind(intersections,c(x,eq[1]*x+eq[2]))
});
}
});
# Get linearLines intersections
if(NROW(linearLines)>1){
for(j in 1:(NROW(linearLines)-1)){
mainLL=c(linearLines[j,1],linearLines[j,2]);
for(k in (j+1):(NROW(linearLines))){
slaveLL=c(linearLines[k,1],linearLines[k,2]);
toSolve=matrix(c(-mainLL[1],-slaveLL[1],1,1), ncol=2,nrow=2);
tryCatch({
solution=solve(toSolve,c(mainLL[2],slaveLL[2]))
intersections=rbind(intersections,solution)
},error=function(error){});
}
}
}
}
# Build solution, if we have intersections
if(NROW(intersections)>0){
currentSol=c(mean(intersections[,1]),mean(intersections[,2]));
sol=cbind(sol,currentSol);
}
# If we don't have intersections (middle of segment)
else{
if(NROW(linearLines)>0||length(xLines)>0){
currentSol=getMiddleOfSegment(
circlesIntersections[1,1],circlesIntersections[1,2],
circlesIntersections[2,1],circlesIntersections[2,2]
);
# sol=cbind(sol,currentSol);
}
}
# If we plot current solution
if(stepByStep){
# Plot gateways
plot(gwX,gwY,asp=1,xlim=c(-precisionPlot,precisionPlot),ylim=c(-precisionPlot,precisionPlot),pch=17, col="orange")
# Plot circles
for(j in 1:nbGw){
draw.circle(gwX[j],gwY[j],distances[j,i],lwd=0.5);
}
# Plot circles intersections
if(!is.null(circlesIntersections)){
apply(circlesIntersections,1,function(row){
lines(row[1],row[2],type="p",col="blue",pch=20)
});
}
if(!is.null(intersections)){
apply(intersections,1,function(row){
lines(row[1],row[2],type="p",col="black",pch=20)
});
}
if(!is.null(linearLines)){
apply(linearLines,1,function(row){
abline(row[2],row[1]);
});
}
if(!is.null(xLines)){
sapply(xLines,function(x){
abline(v=x);
});
}
if(!is.null(sol)){
lines(sol[1],sol[2],type="p",col="red", pch=16)
}
readline(prompt = "Press enter for next step...")
}
}
return(sol);
}
##############################
# Multilateration avec optimisation de la taille des cercles (prendre le plus petit rayon possible)
# radiusStep = pas de réduction de la taille du rayon
##############################
optimizeRadius=function(gwX,gwY,distances,stepByStep=FALSE,precisionPlot=80, radiusStep=1,zeroForNull=FALSE){
sol=NULL;
for(i in 1:NCOL(distances)){
factor=0
curDistances=as.matrix(distances[,i])-factor
# Try to find solution without optimisation (factor=0)
estimated=multilateration(gwX,gwY,curDistances,stepByStep=stepByStep,precisionPlot=precisionPlot)
# Repeat multilateration until radius = 0
while(sum(curDistances<=0)!=NROW(gwX)){
factor=factor+radiusStep
curDistances=curDistances-factor # Reduce circles radius
curDistances[curDistances<0]<-0 # Put zero in negative radius
e=multilateration(gwX,gwY,curDistances,stepByStep=stepByStep,precisionPlot=precisionPlot) # Temporary solution
if(!is.null(e)){ # A better solution is found
estimated=e
}
else if(!is.null(estimated)){ # No other solution is possible
break;
}
}
if(zeroForNull && is.null(estimated)){
sol=cbind(sol,c(0,0))
}
else{
if(!is.null(estimated)){
sol=cbind(sol,estimated)
}
}
}
return(sol)
}
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