Calculate distance from ratio between three points.

[frankzappa]

Hello.
I’m wondering if it’s possible to calculate coordinates to a point in a 2D plane given the following:

I have three signal sensors lets call them a, b and c.

b is placed on the y axis 10 centimeter from the origin (x,y = 0,10), c on the x axis 10 centimeter from origin (x,y = 10,0) and a on the origin (x,y = 0,0).

The point I want to calculate gives out a signal and I only know the ratio of the signal strength between any of the three sensors ab, ac or bc from the point to the sensors.

Is it possible to calculate the coordinates to the point given these values or do I need more sensors.

note that I only need to calculate positions in positive xy values.

Please forgive me if I’m not using the correct terms as I don’t know much about math and need this to solve a real world problem.

Thanks

Enes

 

[MarkFL]

Hello, and welcome to FMH!

Do you know how signal strength varies as a function of the distance from the source?

 

[frankzappa]

Hello, and welcome to FMH!

Do you know how signal strength varies as a function of the distance from the source?

Thank you ?

The only info I can use is the signal velocity difference between any of the three signals.


I’m trying to make an electronic drum. I want to sense the position of every strike and every strike has different velocity.

I have 5 sensors on the whole drum head and the three in question here are one quadrant of the drum head. (Drum head is a circle).

I could also maybe use the time delay between signals or time of arrival but I haven’t experimented yet if the delay is measurable. It probably is.

 

[Mr. Bland]

What you're looking to do is a form of multilateration, where multiple observers might know the distance from themselves to a point of interest, but only by considering more observers can the exact position be determined.

This can be accomplished in your situation, provided you can determine the distance to the point of interest from each observer. You've stated that you can determine the signal strength from that point, which you will need to be able to convert into a distance (a process that depends on the properties of the signal and the medium carrying it). Once you can convert the signal strength into distance, you can find the position of the point.

Each observer will know the distance from itself to the point of interest. A circle drawn about the observer with that distance as its radius will give all of the points where the signal may have originated. If two observers are present, then the places where the circles intersect will be the only points where the signal may have originated. If three or more observers are present, then all circles will intersect at exactly one point, the origin of the signal.

 

[frankzappa]

What you're looking to do is a form of multilateration, where multiple observers might know the distance from themselves to a point of interest, but only by considering more observers can the exact position be determined.

This can be accomplished in your situation, provided you can determine the distance to the point of interest from each observer. You've stated that you can determine the signal strength from that point, which you will need to be able to convert into a distance (a process that depends on the properties of the signal and the medium carrying it). Once you can convert the signal strength into distance, you can find the position of the point.

Each observer will know the distance from itself to the point of interest. A circle drawn about the observer with that distance as its radius will give all of the points where the signal may have originated. If two observers are present, then the places where the circles intersect will be the only points where the signal may have originated. If three or more observers are present, then all circles will intersect at exactly one point, the origin of the signal.

I have read about that but the problem is that the signal is a vibration picked up by piezo sensors. The vibration is a drum stick hit on a drum played by a human. The velocity is never constant.

 

[Mr. Bland]

That changes things slightly, but it can still be done. Although the amplitude of the sound will vary, it should still take the same amount of time to travel 1 unit of distance in all cases (speed of sound in the atmosphere at your location). The observers, however, won't be able to directly compute the distance to the drum based on the sound alone.

When there are multiple observers, the signal is likely to reach them at different times. This difference in time is multiplied by the speed to determine the difference in distance. The distances from each observer can then be calculated, because there is a finite set of positions where the signal could have originated. When there are three or more observers (that aren't right on top of one another), there can only be one such position.

 

[frankzappa]

That changes things slightly, but it can still be done. Although the amplitude of the sound will vary, it should still take the same amount of time to travel 1 unit of distance in all cases (speed of sound in the atmosphere at your location). The observers, however, won't be able to directly compute the distance to the drum based on the sound alone.

When there are multiple observers, the signal is likely to reach them at different times. This difference in time is multiplied by the speed to determine the difference in distance. The distances from each observer can then be calculated, because there is a finite set of positions where the signal could have originated. When there are three or more observers (that aren't right on top of one another), there can only be one such position.

Cool, so I should measure the speed of the signal and learn about multilateration. This was really helpful. Thanks

 

[Mr. Bland]

Specifically, you'll want to find the radius of the "first" observer's circle such that all three circles intersect. They will only do this at one point, and only for one radius of the first circle. This will involve a system of circular equations. [MATH](x - center_{x})^2 + (y - center_{y})^2 = radius^2[/MATH]

 

[frankzappa]

Specifically, you'll want to find the radius of the "first" observer's circle such that all three circles intersect. They will only do this at one point, and only for one radius of the first circle. This will involve a system of circular equations. [MATH](x - center_{x})^2 + (y - center_{y})^2 = radius^2[/MATH]

I understand, every signal is basically a radus of a circle and I need to find where the circumferences of the three circles intersect. Thank you

 

[Deleted member 4993]

Cool, so I should measure the speed of the signal and learn about multilateration. This was really helpful. Thanks

No ... NOT the speed of the signal. You'll need to measure the intensity of the signal. The intensity of the signal varies inversely proportional to the square of the distance (1/r²).

If your signal source is "sound" and you are detecting the pressure of "pressure waves" then the magnitude of pressure becomes inversely proportional to the distance (1/r). Read https://en.wikipedia.org/wiki/Inverse-square_law as a starting point.

 

[Mr. Bland]

No ... NOT the speed of the signal. You'll need to measure the intensity of the signal.

This is incorrect. As stated, the signal's amplitude is not consistent because the source (human playing a drum) is not consistent, and therefore is insufficient for measuring the distance to the signal's source. However, the speed of sound--especially on the scale of something like listening for the sound of a drum--is very consistent and, in conjunction with multiple listeners, is sufficient for locating the origin of the signal.

 

[Deleted member 4993]

This is incorrect. As stated, the signal's amplitude is not consistent because the source (human playing a drum) is not consistent, and therefore is insufficient for measuring the distance to the signal's source. However, the speed of sound--especially on the scale of something like listening for the sound of a drum--is very consistent and, in conjunction with multiple listeners, is sufficient for locating the origin of the signal.

OP intended to (at least I understood) measure the "difference in speed" to calculate the location.
"Cool, so I should measure the speed of the signal and ...." (response 7)
I was trying to convey that the speed does not change from location to location of sensing (unless the property of the medium changes). I am not sure why the intensity will be inconsistent while measuring the same "strike" - with different sensors. As I understood the OP is trying to locate the "strike" on the drum.