I will try to explain again
I think my earlier explanation was correct. Either it was not correct, or I did not explain it well enough. I did not write out the math, I figured you only needed help with the concept.
You can draw this out on paper to make it easier to understand.
To make it easier to think about first use the speed as 1 m/s.
Think of a box as the upper right area of a coordinate system. Where the first reciever is at point (0,0). Then think of reciever 2 at point (0,10) and reciever 3 at (10,0).
Now take the difference between the time at reciever 1 and reciever 2.
From just this information you will be able to find a list of solutions, which will all fall on a line.
For example, one possible solution is where the transmitter is on the line between point 1 and point 2. We know the total distance between point 1 and point 2 so finding that solution is simple. Say the time difference is 2 seconds (using a speed of 1m/s, the transmitter would be located at (0,4) if it is on the line between the two. So the time between transmission and recieving by reciever 1 is 4 seconds. Now if you supposed that the time between transmission and reception by reciever one is 5 seconds you also know that the time between transmission and reception by reciever 2 is 7 seconds. You can create a triangle then with sides of 10, 5, and 7. You can then figure the height of the triange and get the exact coordinates for this solution. Once you have two points you can find the equation of the line.
Once you have the line equation of all possible solutions for point 1 and 2, then do the same between points 1, and 3.
Now you have the equations for two lines and only have to solve for their intersection.
You still have to put in the math, but I think this should cover the idea of how to solve the problem. I feel pretty sure this solution would work, if someone knows otherwise, feel free to trash my solution.
I will try to explain again
I think my earlier explanation was correct. Either it was not correct, or I did not explain it well enough. I did not write out the math, I figured you only needed help with the concept.
You can draw this out on paper to make it easier to understand.
To make it easier to think about first use the speed as 1 m/s.
Think of a box as the upper right area of a coordinate system. Where the first reciever is at point (0,0). Then think of reciever 2 at point (0,10) and reciever 3 at (10,0).
Now take the difference between the time at reciever 1 and reciever 2.
From just this information you will be able to find a list of solutions, which will all fall on a line.
For example, one possible solution is where the transmitter is on the line between point 1 and point 2. We know the total distance between point 1 and point 2 so finding that solution is simple. Say the time difference is 2 seconds (using a speed of 1m/s, the transmitter would be located at (0,4) if it is on the line between the two. So the time between transmission and recieving by reciever 1 is 4 seconds. Now if you supposed that the time between transmission and reception by reciever one is 5 seconds you also know that the time between transmission and reception by reciever 2 is 7 seconds. You can create a triangle then with sides of 10, 5, and 7. You can then figure the height of the triange and get the exact coordinates for this solution. Once you have two points you can find the equation of the line.
Once you have the line equation of all possible solutions for point 1 and 2, then do the same between points 1, and 3.
Now you have the equations for two lines and only have to solve for their intersection.
You still have to put in the math, but I think this should cover the idea of how to solve the problem. I feel pretty sure this solution would work, if someone knows otherwise, feel free to trash my solution.
Re: I will try to explain again
Quote:
Originally posted by savageag
I think my earlier explanation was correct. Either it was not correct, or I did not explain it well enough. I did not write out the math, I figured you only needed help with the concept.
You can draw this out on paper to make it easier to understand.
To make it easier to think about first use the speed as 1 m/s.
Think of a box as the upper right area of a coordinate system. Where the first reciever is at point (0,0). Then think of reciever 2 at point (0,10) and reciever 3 at (10,0).
Now take the difference between the time at reciever 1 and reciever 2.
From just this information you will be able to find a list of solutions, which will all fall on a line.
For example, one possible solution is where the transmitter is on the line between point 1 and point 2. We know the total distance between point 1 and point 2 so finding that solution is simple. Say the time difference is 2 seconds (using a speed of 1m/s, the transmitter would be located at (0,4) if it is on the line between the two. So the time between transmission and recieving by reciever 1 is 4 seconds. Now if you supposed that the time between transmission and reception by reciever one is 5 seconds you also know that the time between transmission and reception by reciever 2 is 7 seconds. You can create a triangle then with sides of 10, 5, and 7. You can then figure the height of the triange and get the exact coordinates for this solution. Once you have two points you can find the equation of the line.
Once you have the line equation of all possible solutions for point 1 and 2, then do the same between points 1, and 3.
Now you have the equations for two lines and only have to solve for their intersection.
You still have to put in the math, but I think this should cover the idea of how to solve the problem. I feel pretty sure this solution would work, if someone knows otherwise, feel free to trash my solution.
Thank you for you reply.
I do not think your solution is correct.
Let me give you an example to try out, say I send out a pulse at an unknow time. This signal is picked up by each receiver at these times here:
receiver1 : 212,8284 seconds
receiver2 : 218,24621 seconds
receiver3 : 218,24621 seconds
receiver4 : 221,3137 seconds
The actual time isnt relevant in this context but the relationship between the four times is very important. So I could simply write,
receiver1 : 0
receiver2 : 5,4178
receiver3 : 5,4178
receiver4 : 8,4853
You can then calculate part of the distance from receiver2, receiver3 and receiver4 to the object. You dont not however know the distance between the object and receiver1. So I guess you can setup an equation that looks something like this :
dr1 = distance from object to receiver1
dr1 = x
dr2 = x + (5,4178 * 1m/s)
dr3 = x + (5,4178 * 1m/s)
dr4 = x + (8,4853 * 1m/s)
But how far does this get us ?
The area is 10*10 meters long. The speed is set to 1m/s.
Can you now please figure out what the position of the object was when sending the signal ?
Receiver1 is located at (0,0)
Receiver2 is located at (10,0)
Receiver3 is located at (0,10)
Receiver4 is located at (10,10)
Really appreciate everyones help.
Btw, I do know the answer to the above question just like to see if anyone manages to figure it out without me giving any clues.
Will you ever know the answer?
laasunde,
Will you ever know the answer to the problem you outlined?
Is that something you were doing in school? If so, will the professor give the elegant answer?
Did you use the code given as your answer? If not, did you find a better way to solve the problem?
I think it would be nice to answer these questions for the people who took the time to work on your problem.