How would one calculate the distance and bearing of a signal source?

• I
• KevinTOC
In summary, you can use the inverse square law to calculate the distance to a signal source if you know its signal strength and the direction it is facing.
KevinTOC
Basically, I'm wondering how you can essentially determine the bearing of a signal source, if you know its signal strength.

assuming you're in a vacuum, and you have a beacon transmitting a signal, and you know its signal strength. How could you find out the bearing (direction) it's at, if you know its signal strength, and if which way you're facing is 0°?

I've tried figuring it out myself, but I just can't get the final stuff:

Assuming the signal strength is 100k
The inverse square law says intensity = 1/distance^2 Therefore, Distance = sqrt(1/Intensity)
Therefore, distance (D) would be: sqrt(1/100k) = 0.003162
The distance is the Hypotenuse (a)
Therefore, c (the shortest side) = a/2 since in a right angled triangle, the hypotenuse is always double as long as the shortest side. Therefore, c = 0.001581
b
(The last side) is therefore sqrt(0.003162^2-0.001581^2) = 0.002738
The area of the triangle is A = (b*c)/2 = 0.000002 (2 x 10^-6)

The part I'm stuck on, is how to calculate angle ca? sin (0.001581/0.003162) Gets the angle 0.479426° Which doesn't seem right, since according to Google, it's supposed to be 53.14°

(If this is in the wrong forum category, I'm sorry.)

KevinTOC said:
intensity = 1/distance^2
The inverse square law is actually: I ∝1/D2, where ∝ means "is proportional to". To know the recveived intensity,[meant to say "distance"] you need the [received intensity], source intensity and the propagation model (spherical, cylindrical..). You also need to add some kind of diagram to clarify your scenario. Do you have multiple receivers?

Last edited:
KevinTOC said:
Therefore, c (the shortest side) = a/2 since in a right angled triangle, the hypotenuse is always double as long as the shortest side.

That's not true at all!

If we have an angle less than 45 degrees, then the opposite of that angle will be the shortest side. Since that angle can be anything in the range ##0^\circ < \theta < 45^\circ##, the ratio opposite/hypotenuse ##= \sin(\theta)## can be anything in the range ##0 < \sin(\theta) < 0.7071067## ... It definitely is not required to be 0.5.

Also this is wrong:
KevinTOC said:
The inverse square law says intensity = 1/distance^2 Therefore, Distance = sqrt(1/Intensity)

As @lewando points out, the inverse square law says that intensity is proportional to ##1/d^2##, not equal. So if you know that the intensity is 1/100 of the intensity at, say, 2 m, then you know that your distance is ##\sqrt{100}## or 10 times as far as 2 m. In other words, it means you are 20 m from the source. Notice that to do that calculation, you need something to compare with, such as the intensity at a different known distance.

You can also calculate the distance if you know the total emitted power and the shape into which that power is being emitted. For instance, if you assume that it is spread out over a hemisphere, then you divide the total power by the area hemisphere of radius ##r## to get the power per unit area (intensity) at distance ##r## from the source.

But even once you know the distance, that doesn't answer your question. If I tell you something is 100 m away from you, does that identify only one possible location? Is there only one point in space which is 100 m from you?

With multiple power measurements, the problem is solvable.

jedishrfu said:
You need to use a directional antenna to find the bearing.

https://en.m.wikipedia.org/wiki/Directional_antenna

That's the standard approach. But if you are able to determine the distance to multiple receive points based on power measurements, you can geolocate the source that way as well.

Yes, of course. I didn't know that was an option it seemed the OP wanted to know how to do from a single point.

It wasn't mentioned by the OP but I've been involved in more than one project professionally to do just that kind of estimation, so it's of personal interest

This wikipedia source mainly deals with antenna array transmission. Similar technology used as passive receivers on your spacecraft might be able to help locate a beacon in space. If not phase, then other differences among your antennae as the beacon RF impinges, could provide gross localization. The diagram shows a linear array but spheroids constructed of hexagonal sections resembling a radome could be used, particularly if comparing beacon signal strength instead of phase. Advantage over a rotating directional antenna receiver is that the array remains fixed to the moving spacecraft .

1. How do you calculate the distance of a signal source?

To calculate the distance of a signal source, you would need to know the signal's frequency and the propagation speed of the medium it is traveling through. Using the formula Distance = (Speed of Light/Frequency) x Time, you can calculate the distance by measuring the time it takes for the signal to travel from the source to the receiver.

2. What is the bearing of a signal source?

The bearing of a signal source refers to the direction from which the signal is coming from. This can be determined by using a compass or other directional tools to measure the angle between the signal source and the receiver.

3. How can you calculate the bearing of a signal source?

To calculate the bearing of a signal source, you would need to know the location of the receiver and the direction of the signal source. Using trigonometry, you can calculate the bearing by finding the angle between the two points.

4. What factors can affect the accuracy of distance and bearing calculations?

There are several factors that can affect the accuracy of distance and bearing calculations, including atmospheric conditions, interference from other signals, and the quality of the equipment being used. Additionally, the curvature of the Earth and the presence of obstacles can also impact the accuracy of these calculations.

5. Are there any alternative methods for calculating the distance and bearing of a signal source?

Yes, there are alternative methods for calculating the distance and bearing of a signal source, such as using triangulation with multiple receivers or using specialized equipment like radar or sonar. However, these methods may require more advanced technology and may not be as accessible as traditional methods.

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