how to find the coordinates of sensor nodes deployed with Gaussian distribution

how to find the coordinates of sensor nodes deployed with Gaussian distribution in a plane.

Answer 1

[Roger Stafford]

I assume the variance of the distribution is to be the same in all directions on the plane, namely s^2. There has to be some point of the plane which is at the mean (central) point of the distribution. Call this point P0 = [x0,y0,z0]. Suppose the equation of the plane in question is a*x+b*y+c*z+d = 0. Let n denote the number of nodes. Then do this:

 N = null([a,b,c]); % Choose two orthonormal vectors orthogonal to [a,b,c]
 P = bsxfun(@plus,P0,s*randn(n,2)*N.'); % Generate random points on the plane

P will be an n-by-3 matrix in which the rows are coordinates of points distributed on the plane with the above Gaussian distribution. You can display them with:

 plot3(P(:,1),P(:,2),P(:,3),'y.')

[Anil]

Thanks