geometry - How to determinate position of a point with triangulation -
i working on project of localization wireless sensors network. using triangulation method estimate position of wireless sensors, have 2 sensors position known : a(x1,y1) and b(x2,y2) and point want locate c(x,y) and have distances between points : ab, ac & bc how can triangulation ? put a := dist(b,c), b := dist(a,c). := (a1,a2), b := (b1,b2), c := (x,y). we have (x - a1)^2 + (y - a2)^2 = b^2 eq (1) (x - b1)^2 + (y - b2)^2 = a^2 thus: x^2 -2(a1)x + (a1)^2 + y^2 -2(a2)y + (a2)^2 = b^2 x^2 -2(b1)x + (b1)^2 + y^2 -2(b2)y + (b2)^2 = a^2 now subtract: (2(b1) - 2(a1))x + (a1)^2 - (b1)^2 + 2((b2) - (a2))y + (a2)^2 - (b2)^2 = b^2 - a^2 solve y : y = u + vx eq (2) where: u := ((a1)^2 + (a2)^2 - ((b1)^2 + (b2)^2) + a^2 - b^2)/(2((a2) - (b2))) v := (2((b1) - (a1)))/(2((a2) - (b2))) replace y u + vx in eq 1 above: (x - a1)^2 + (u + vx - a2)^2 = b^2 rx^2 + sx + t = 0 where: r :=...