localization, triangulation, image inspection

[systems_eng]

I'm trying to locate a RF transmitter, and I'm not exactly sure what the easiest method would be.

Right now I sampling gps and rssi data from a single transmitter.  Looking at the image I have attached, I have graphed the sampled points (light blue), the transmitter (white) and rssi for the corresponding samples (dark blue circles).  The transmitter that is shown in the image is what I'm trying to locate.  It is shown in the image to get a better sense of what area I should be trying to focus on.  These circles are just a rough estimate of what the rssi values would look like, just to show the relationship between distance and rssi... which I'm still trying to work on.  But before I went any further, I was curious if there was any way to solve this problem through the following methods:

localization: finding the most common point of intersection between the circles

image inspection: some how finding the greatest number of overlapping regions of each circle, then finding the centroid of that region.

Since I don't know the direction of the rssi vector, there isn't any sort of angle that I can use - so the circles seem like the best bet.  I've been working at this for a while and reall have come to a wall.  Any ideas or suggestions?

[SteelStonehenge]

I don't think we have nearly enough information to help you solve this.  What frequency range is your transmitter?  Are we talking about location over a distance of yards or hundreds of miles?  What GPS data are you getting from the transmitter?  If you have GPS data, you already know where it is, I'd assume.

Locating distance to a transmitter by relative signal strength is nigh unto impossible.  If you PRECISELY know the transmitted ERP, and you have a CLEAR FREE SPACE path between you and the transmitter, you MIGHT come up with a crude estimate using the inverse square power attenuation.  Assuming the transmitter is on the surface of the earth, you need at least two-point triangulation.  If it is at an  unknown altitude, you will need three point triangulation.

Some actual details on the experiment will help us a lot.

eric

[SteelStonehenge]

Another useful hint:

      There is only one  method of locating a transmitter when you have no information about the transmitter itself: plain old triangulation.  With straight triangulation you don't need to know what the power level is, what the antenna radiation pattern is (assuming the device is small enough to be considered a point source), or worry about non-linear propagation paths (with certain caveats).

     No matter how sophisticated your number crunching is, you still have to work within the laws of physics.  From a single location, you can only determine four things about a radio wave, its frequency, it's direction of arrival, its polarization, and its intensity (at that point).  (Even that's not strictly true....an antenna capable of determining direction or polarization has to be  finite size...)

eric

[systems_eng]

The transmitter is running at 900MHz.

The distance should only be miles (think blocks of a neighborhood).

I'm capturing data from a transmitter and a GPS receiver simultaneously, attaching the two data packets as I move.

I already know where my transmitter is located.  I'm sampling / testing around it to figure out if I can find the transmitter by using these location methods.

The data that I’m post processing is the following:

-          RSSI

-          Latitude

-          Longitude

-          (Altitude is a possibility, but since I’m sampling in a remotely level environment, I excluded this from my calculations)

I was originally thinking of retrieving these radio packets, then attaching them to a latitude and longitude at the captured coordinate.  Taking the RSSI data from the radio packet, I would be able to assign an intensity value to the GPS coordinate.  These intensities would represent a radial circle, which the transmitter and reader would be able to communicate within.  Radial distances would then determine the distance between each sample and the transmitter.  I was hoping through localization, I would be able to find the most common point of intersection between the RSSI circles.

I realize that clear space is no where near the conditions that I will see in the field.  But I have some algorithms that will help deal with clutter, to better predict the distance between the transmitter and reader.

I guess some of my problems are that I’m probably seeing some signal reflections, when testing in the field.  There are multiple occasions where I’m sampling from different distances, but receiving the same or similar RSSI values.  I was thinking that the most common radial circle intersection point would exclude these erroneous signals.  This seems like a reasonable solution to me, but I can’t think of an efficient way of finding this point.

Recently I’ve been poking around interpolation and 2D meshing to see if I could make better progress in those areas, but I haven’t found anything.  Hopefully this is enough information; just ask if you need more.  I appreciate the help.

[SteelStonehenge]

OH.   The GPS receiver is with YOU.    Well that makes things a LOT clearer now. 🙂   It will at least remove one source of error for triangulations.  However, you still have the issue of determining direction from any of your monitoring points.  There is no way this can be done without a directional receive antenna (which will also help with eliminating, or at least identifying, reflections).  I can assure you that RSSI information is of ZERO value for this exercise.

Eric

[SteelStonehenge]

Just for the sake of argument.

     Okay, I'll cut you some slack.   Let's assume that RSSI signals ARE valid.  In that case, the problem would be so simple as to be trivial.  All you'd need is to locate three points on  any equal field intensity circle (assuming your transmitter is omnidirectional).  Draw a chord between point 1 and point 2.   Draw another chord between point 2 and point 3.  Bisect each of the chords.  Where the two bisectors intersect is where your transmitter is.   Problem done.

eric  

[systems_eng]

That's what I figured, just a form of triangulation.  I guess the only problem with this method, is that the accuracy of the determined location, will heavily rely on the reliability of the sampled RSSI values (which have shown to vary).  In order to handle inaccurate RSSI values, I would sample say 20 times instead of 3, then find the most common intersection.  But if I have 20 sampled points, 20 distance circles, roughly 100 points per circle... that would be a lot of matching.  I guess I will try to work on this method.  Thanks.

[SteelStonehenge]

I think you're doing way overkill here, and probably a lot of the oversampling would be counterproductive.  Three points on each radial (each radius being a multiple of your first estimate) should be MORE than enough.   I spent twenty years doing AM broadcasting antenna proofs using far fewer points than you're suggesting.  I'd try to get the points separated by close to 120 degrees (which you can only determine by a first estimate "shotgun" approach), and then get a couple more radii.  Or better yet, use a directional antenna on your receiver and be done with it!

Eric