Please find the attached tutorial

page 3;

To plot a rotated hyperbola, it is neces-

sary to do a coordinate transformation. The

transformation used to plot the hyperbola cor-

responding to a particular baseline takes points

calculated in an x, y coordinate system in which

the baseline is vertically upward (in which the

hyperbolae are easy to calculate), and rotates

the points clockwise by an angle ¸ so that the y22

axis is correctly oriented with the actual base-

line in the networks x, y coordinate system. It

then offsets the resulting points away from be-

ing centered around (0,0) to the center (x0, y0)

of the actual baseline. From a carefully drawn

sketch of the geometry of the (22) to (2) trans-

formation, determine the matrix expression for

onverting (x22, y22) values to (x2, y2) values, and

confirm that it is the same as used in the trans-

form program

You need to find the matrix co-

efficients so that:

x2 a11 a12 y22

y2 = a21 a22 = x22

Can someone please explain this to me... why do we need to rotate the hyperbola?

Your help would be really appreciated... thanks in advance.

toa.pdf
http://www.experts-exchange.com/images/122524/pic.png

Suppose you have RX1 at (0,10) and RX2 at (0,0). The DTOA (t1-t2) is 4 ns.

You have no other information.

Can you sketch the locus of possible TX positions?

Can you use a compass to construct 3-5 points of the curve?

It will be half of a hyperbola. Do you understand why it only half?

Can you get the equation of the hyperbola using the distance formula and algebra?

Can you get the equation into standard form?

Maybe something like (y-a)² - (x-b)² = c²

==========================

Now suppose you have RX2 at (0,0) and RX3 at (10,10). The DTOA (t2-t3) is 9 ns.

You should still be able to sketch the curve and derive an equation for it.

But you won't be able to get into a standard form because is not aligned with the axes.

Whether or not this matters depends on the problem you are trying to solve and

the technique you want to use.