Android Java Trilateration Method

Question

I have a little problem ... Does anyone know how I can implement this?

I need a method in java:

public /*COORDINATE OBJECT*/ getTrilaterationPointBetween( /*COORDINATE OBJECT*/ coordinate1, double distance1, /*COORDINATE OBJECT*/ coordinate2, double distance2, /*COORDINATE OBJECT*/ coordinate3, double distance3){ //MAGIC return /*COORDINATE OBJECT*/; } 

In practice, this method will get 3 coordinates and the distance between "myLocation" with one of them ...

I need a Trilateration algorithm !!

I did some searches and did some tests, and the results led me to the middle of the peace!

About OBJECT, really simple, have 2 variables representing latitude and longitude.

I tried this method:

 static double[] MyTrilateration(Ponto ponto1, double dist1, Ponto ponto2, double dist2, Ponto ponto3, double dist3) { double[] tmpWAP1 = new double[3]; double[] tmpWAP2 = new double[3]; double[] tmpWAP3 = new double[3]; double tmpLat2, tmpLong2, tmpLat3, tmpLong3; double tmpSlide, deg; double MyLat, MyLong; double[] MyLocation = new double[2]; tmpLat2 = ponto2.getX() - ponto1.getX(); tmpLong2 = ponto2.getY() - ponto1.getY(); tmpLat3 = ponto3.getX() - ponto1.getX(); tmpLong3 = ponto3.getY() - ponto1.getY(); tmpSlide = Math.sqrt(Math.pow(tmpLat2,2)+Math.pow(tmpLong2,2)); deg = (180/Math.PI)*Math.acos( Math.abs(tmpLat2)/Math.abs(tmpSlide)); if( (tmpLat2>0 && tmpLong2>0) ) { deg = 360 - deg; } else if( (tmpLat2<0 && tmpLong2>0) ) { deg = 180 + deg; } else if( (tmpLat2<0 && tmpLong2<0)){ deg = 180 - deg; } else if( (tmpLat2>0 && tmpLong2<0)) { deg = deg; } tmpWAP1[0] = 0.0; tmpWAP1[1] = 0.0; tmpWAP1[2] = dist1; tmpWAP2 = myRotation(tmpLat2, tmpLong2, dist2, deg); tmpWAP3 = myRotation(tmpLat3, tmpLong3, dist3, deg); MyLat = (Math.pow(tmpWAP1[2],2)-Math.pow(tmpWAP2[2],2)+Math.pow(tmpWAP2[0],2))/(2*tmpWAP2[0]); MyLong = (Math.pow(tmpWAP1[2],2)-Math.pow(tmpWAP3[2],2)-Math.pow(MyLat,2) +Math.pow(MyLat-tmpWAP3[0],2)+Math.pow(tmpWAP3[1], 2))/(2*tmpWAP3[1]); MyLocation = myRotation(MyLat, MyLong, 0, -deg); MyLocation[0] = MyLocation[0] + ponto1.getX(); MyLocation[1] = MyLocation[1] + ponto1.getY(); return MyLocation; } 

and this method:

 public String getCoordinateWith( Ponto a, Ponto b, Ponto c, Float dA, Float dB, Float dC) { Float W, Z, x, y, y2; W = dA*dA - dB*dB - a.getX()*a.getX() - a.getY()*a.getY() + b.getX()*b.getX() + b.getY()*b.getY(); Z = dB*dB - dC*dC - b.getX()*b.getX() - b.getY()*b.getY() + c.getX()*c.getX() + c.getY()*c.getY(); x = (W*(c.getY()-b.getY()) - Z*(b.getY()-a.getY())) / (2 * ((b.getX()-a.getX())*(c.getY()-b.getY()) - (c.getX()-b.getX())*(b.getY()-a.getY()))); y = (W - 2*x*(b.getX()-a.getX())) / (2*(b.getY()-a.getY())); //y2 is a second measure of y to mitigate errors y2 = (Z - 2*x*(c.getX()-b.getX())) / (2*(c.getY()-b.getY())); y = (y + y2) / 2; return "Position: " + x + " , " + y; } 

Thanks!

Answer 1

I understood! This is my method, it works for me, not 100% more accurate! Works with z = 0 and with only three different points (2D coordinates).

The Ponto class is a simple class with two values ​​(X and Y / Lat and Lon), double.

 public static Ponto getLocationByTrilateration( Ponto ponto1, double distance1, Ponto ponto2, double distance2, Ponto ponto3, double distance3){ //DECLARACAO DE VARIAVEIS Ponto retorno = new Ponto(); double[] P1 = new double[2]; double[] P2 = new double[2]; double[] P3 = new double[2]; double[] ex = new double[2]; double[] ey = new double[2]; double[] p3p1 = new double[2]; double jval = 0; double temp = 0; double ival = 0; double p3p1i = 0; double triptx; double xval; double yval; double t1; double t2; double t3; double t; double exx; double d; double eyy; //TRANSFORMA OS PONTOS EM VETORES //PONTO 1 P1[0] = ponto1.getX(); P1[1] = ponto1.getY(); //PONTO 2 P2[0] = ponto2.getX(); P2[1] = ponto2.getY(); //PONTO 3 P3[0] = ponto3.getX(); P3[1] = ponto3.getY(); //TRANSFORMA O VALOR DE METROS PARA A UNIDADE DO MAPA //DISTANCIA ENTRE O PONTO 1 EA MINHA LOCALIZACAO distance1 = (distance1 / 100000); //DISTANCIA ENTRE O PONTO 2 EA MINHA LOCALIZACAO distance2 = (distance2 / 100000); //DISTANCIA ENTRE O PONTO 3 EA MINHA LOCALIZACAO distance3 = (distance3 / 100000); for (int i = 0; i < P1.length; i++) { t1 = P2[i]; t2 = P1[i]; t = t1 - t2; temp += (t*t); } d = Math.sqrt(temp); for (int i = 0; i < P1.length; i++) { t1 = P2[i]; t2 = P1[i]; exx = (t1 - t2)/(Math.sqrt(temp)); ex[i] = exx; } for (int i = 0; i < P3.length; i++) { t1 = P3[i]; t2 = P1[i]; t3 = t1 - t2; p3p1[i] = t3; } for (int i = 0; i < ex.length; i++) { t1 = ex[i]; t2 = p3p1[i]; ival += (t1*t2); } for (int i = 0; i < P3.length; i++) { t1 = P3[i]; t2 = P1[i]; t3 = ex[i] * ival; t = t1 - t2 -t3; p3p1i += (t*t); } for (int i = 0; i < P3.length; i++) { t1 = P3[i]; t2 = P1[i]; t3 = ex[i] * ival; eyy = (t1 - t2 - t3)/Math.sqrt(p3p1i); ey[i] = eyy; } for (int i = 0; i < ey.length; i++) { t1 = ey[i]; t2 = p3p1[i]; jval += (t1*t2); } xval = (Math.pow(distance1, 2) - Math.pow(distance2, 2) + Math.pow(d, 2))/(2*d); yval = ((Math.pow(distance1, 2) - Math.pow(distance3, 2) + Math.pow(ival, 2) + Math.pow(jval, 2))/(2*jval)) - ((ival/jval)*xval); t1 = ponto1.getX(); t2 = ex[0] * xval; t3 = ey[0] * yval; triptx = t1 + t2 + t3; retorno.setX(triptx); t1 = ponto1.getY(); t2 = ex[1] * xval; t3 = ey[1] * yval; triptx = t1 + t2 + t3; retorno.setY(triptx); return retorno; }