Hi...
I want to do the following using Matlab.
I want to localize a point on 2D plane using trilateration which demands for the distance measure between the unknown point and three known locations. Here is how i have done it(but i think its quite weird way of doing it)
As the unknown point is only "assumed" to be unknown and infact we can get coordinates of that point, I used those coordinates to measure the distance and then used that distance in the trilateration algorithm to get the same coordinates. Please find my code in the attached file or at the end of this question.
Time stamps combined with the propagation speed can be used to measure distance between two points but again we must know the locations of the two points in order know the time of reception of a message. I think similar goes for RSSI.
Please suggest how should i do this. The following is the code for trilateration.
%Trilateration
%coordinates of the known nodes A,B,C
xa=0; ya=0;
xb=4; yb=0;
xc=2; yc=-4;
%coordinates of the node on unknown location
x=2; y=5;
% Find distances from the unknown node location to all the 3 transmitters:
da = sqrt((x-xa)^2+(y-ya)^2);
db = sqrt((x-xb)^2+(y-yb)^2);
dc = sqrt((x-xc)^2+(y-yc)^2);
va = ((db*db-dc*dc) - (xb*xb-xc*xc) - (yb*yb-yc*yc)) / 2;
vb = ((db*db-da*da) - (xb*xb-xa*xa) - (yb*yb-ya*ya)) / 2;
temp1 = vb*(xc-xb) - va*(xa-xb);
temp2 = (ya-yb)*(xc-xb) - (yc-yb)*(xa-xb);
% Estimated user position:
yE = temp1 / temp2;
xE = (va - y*(yc-yb)) / (xc-xb);
You could sent out messages and wait for the acknowledgement messages from the unknown node. the distance could be calculated using the speed of transmission methods. But you may need to compensate for the delays and packet losses that happens.
@Abishek Thekkeyil Kunnath Thanks for your reply.
As for the speed of transmission method, here is the problem that i am facing.
All nodes are time synchronized. A beacon is sent with a time stamp indicating time of transmission. The receiver will calculate the distance by multiplying the difference btw transmission time and reception time with propagation delay. This is where things get messy. While implementing this, I'll have to tell the receiver "the reception time". The reception time is a function of the propagation speed of the medium, the transmission time and most importantly the distance(and distance is what i want to calculate. this brings me back to square 1)
As i have to design the whole thing therefore irrespective of which way the message is going(i.e. whether its the message itself of the ACK) the problem remains the same.
This could be done by RSSI only if you know the transmit power of the transmission signal. If you know that , then from received RSSI, you can calculate the distance to which it came from. This is however only possible for transmitter localization and if all nodes have the same transmit power. See one of RSS lateration techniques on Cisco's Website.
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