I understand the tutorial up to this point...

Again saving the program as a separate
file, further modify it to show how the hyper-
bolas corresponding to TOA measurements at
three stations locate a source in two spatial di-
mensions. Let the station locations be at the
vertices of the isosceles triangle x1,y1 = (10,10)
x2,y2 = (+10,10), and x3,y3 = (0,+10) km,
respectively. Use Matlabs input function to
specify a source location (also in km units), and
calculate the times the signal would be received
at each station. Finally, plot the hyperbolae
corresponding to each of the three baselines to
see the solution. Use the pause function in
your for loop to identify each hyperbola as it is
added to the plot. Your plot should look some-
thing like Figure 6.

I have drawn out where I understand the baselines to be.
I not sure where to go from here...

toa.pdf
pic.png
LVL 1
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Commented:
In your tutorial page 2:
"the differences in the arrival times at a pair of stations i,j constrain the source to lie on a hyperboloid of revolution about the baseline between the two stations."
The equation (7) page 3 defined for hyperbola with foci lying on the y axis, this your 2 stations. If they are not on y axis you need to rotate the hyperbola.

So you need to find a and b parameters for your hyperbola. Distance between staitions is 2d, right? You have one equation, but you have 2 unknowns. I didn't go through all the tutorial, so I don't know the answer. Willl think about it.
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Commented:
" Let the station locations be at the
vertices of the isosceles triangle x1,y1 = (10,10)
x2,y2 = (+10,10), and x3,y3 = (0,+10) km,"
---
Two of these points do not appear on your drawing and are actually the same point.
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Commented:
Step 1
"Use Matlabs input function to
specify a source location (also in km units), and
calculate the times the signal would be received
at each station."

Pick a point, any point and do three calculations giving the time a signal from your point would arrive at the three points on your triangle.
t = d/v    where t is the time d is the distance from your triangle point to the point you picked and v is the speed of the signal.

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Commented:
> x1,y1 = (10,10)
It's actually (-10,-10). Minus just was not copied properly.

Do you know how to calculate distance between your points?
Can you calculate angle between each baseline and x axis to determine the rotation?
Did you solve Exercise 3 on page 3 to derive your a and b parameters from the distance?

Before coding in Matlab you need to solve those problems.
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Author Commented:
"Do you know how to calculate distance between your points?"
=> d=sqrt((xi-x)^2+(yi-y)^2)

"Can you calculate angle between each baseline and x axis to determine the rotation?"
=> That is the part I do not understand... why do we rotate? Do we rotate the baseline or calculate the hyperbola then rotate the hyperbola? Is theta the angle between the x axis and the baseline f1f3 the angle between the baseline between the x axis and the baseline f2f3?
theta is calculated with Tan(theta) = Opposite / Adjacent.

"Did you solve Exercise 3 on page 3 to derive your a and b parameters from the distance?"
Is this a+b=sqrt((xi-x)^2+(yi-y)^2) since on pg 3 it says a^2+b^2=d^2?

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Author Commented:
sorry forgot to say, updated screenshot below for the comment above
screener.png
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Commented:
Sorry, you should calculate angle between each baseline (line between 2 stations) and y axis. Because if 2 stations are located on the y axis you don't have to rotate hyperbolas.
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Author Commented:
What do you do after you calculate the angle between the baselines and the y axis?

Why do you rotate in the first place? This is the part I am having difficulty with

Also "Did you solve Exercise 3 on page 3 to derive your a and b parameters from the distance?"
Is this a+b=sqrt((xi-x)^2+(yi-y)^2) since on pg 3 it says a^2+b^2=d^2?
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Commented:
"That is the part I do not understand... why do we rotate?"
You rotate because the program to calculate te hyperbola is written so that the two foci are on the y axis. The result gives you the hyperbola but you have to rotate it to get it to put the real foci in the correct place.
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Author Commented: